The Prime Puzzles and Problems Connection

Problems & Puzzles: Puzzles

1.- The Gordon Lee puzzle

2.- Prime strings

3.- Magic Squares with consecutive primes

4.- Prime - magical squares

5.- Find Pn =prime >61 such that Pn divides Pn+1*Pn+2 + 1

6.- Ray Ballinger suggestion

7.- Palindrome - Primes: 2 questions

8.- Primes by Listing

9.- p1 + p2 + … pk = n m , m => 2

10.- Primes associated to Primorials and Factorials

11.- Distinct, Increasing & Decreasing Gaps

12.- Period Length of 1/p

13.- Magical Pentagrams

14.- Pal-Primes and sum of powers

15.- Narcissistic pal-primes

16.- Consecutive primes and ending-digit

17.- Weakly primes

18.- Some Special Sums of Consecutive Primes

19.- Primes on a Clock

20.- Reversible Primes

21.- Happy Primes

22.- Primes and Persistence

23.- Pal-primes adding consecutive primes

24.- Primes in several bases

25.- Composed primes

26.- Honaker & Jud. McCranie puzzle

27.- Heinz Rectangles

28.- Heinz Stair-case

29.- Pi = P i-1&nxtprm(P i-1), Pi = prime for i => 1

30.- Queen attacking primes in a Knight’s tour solution

31.- The Average Prime number, APN(k) = S(Pk)/k

32.- Find couples of numbers like this (1033, 8) such that:
1033 = 8^1+8^0+8^3+8^3

33.- Find numbers like this:15551(palprime)= Fifteen Thousand Five Hundred Fifty One = 383 (palprime)

34.- Prime Triplets in arithmetic progression

35.- 1999 and the perfect numbers

36.- Sequences of “descriptive primes”

37.- Set of even numbers { ai } such that every ai + aj + 1 is prime

38.- Sloane’s sequences

39.- The Mirrorable Numbers (By Mike Keith)

40. The Pi Prime Search Puzzle (by Patrick De Geest)

41. Palindromic Carnival (dedicated to Patrick De Geest)

42.- This week puzzle is to create a puzzle analog to other one.

43.-Palprime1*Palprime2 = Palindrome

44.-Enoch Haga Puzzle about Consecutive Primes

45.- Prime Solitaire (a puzzle based on a game proposed by Enoch Haga)

46.- Primes expressible as sum of consecutive primes in K ways

47.- p⁴ = a⁴+ b⁴+ c⁴+ d⁴, {a, b, c, d}>0

48.- P³ = a³ + b³ + c³, {P, a, b, c} = primes

49.- “If you are given K numbers of each from 0 to 9, find the maximum quantity of primes that can be formed using those 10K numbers”.

50.- “The best approximation to Pi with primes”

51.- Pi such that Pi is Palprime & i = palindrome

52.- Sum of K consecutive primes equal to the sum of their reversible ones.

53.- Sequences of consecutive economical numbers.

54.- Pair of primes of the form {p, 4p^2+1}

55.- Primes by Generation (Patrick De Geest)

56.- The Honaker's Constant

57.- 8757193191, another little puzzle from Mike Keith

58.- A particular sequence of k consecutive primes (by Enoch Haga)

59.- Six and the nine digits primes (by Jud McCranie)

60.- Generalized Cunningham chain (By Felice Russo)

61.- M(a, p) = a^p - a + 1 ( by Jean Brette)

62.- The qs-sequence, (by T.W.A. Baumann)

63.- Another (3rd) Mike Keith's little puzzle.

64.- The Strange Ruler (TWA Baumann)

65.- Multigrade Relations

66.- The SOPF sequences

67.- The P/M-SOPF sequences

68.- The largest prime magic squares at the end of this Millennium (a puzzle suggested by Jaime Ayala)

69.- Primeful Heterosquares

70.- Primes Double Tree (a puzzle suggested by Paul Leyland)

71.- Consecutive primes and Cunningham chains

72.- Persistent Palprimes

73.- A Collatz-like sequence.

74.- SOD(2^6972593-1)

75.- Prime numbers and the number 2000

76.- z(n)=sigma(n) + phi(n) - 2n

77.- Christmas Prime-Pine

78.- Primes by concatenating consecutive integers

79.- The Chebrakov's - by two months - Challenge

80.- Twin primes - magic squares

81.- Sophie Germain primes - magic squares

82.- The Goldbach Comet

83.- The 6k+1 and 6k-1 boxes

84.- Non-primes adding up to non-primes (by TWA)

85.- A puzzle about the Generalized Mills' theorem

86.- Disjoint sets A & B of consecutive numbers sharing the same set P of prime divisors

87.- Adding prime magic squares (a puzzle suggested by John E. Everett)

88.- A special set of odd primes

89.- The first palprime as a sum of consecutive composites

90.- The prime version of the taxicab problem

91.- Primes with the Smoothest Increasing Digits (SID primes)

92. A pile of prime-spheres

93.- Numbers such that the decimal and hexadecimal representation are the reverse of each other

94. The Domino & the primes

95. K consecutive primes p such that the decimal expansion of the reciprocal 1/p, for each p, has exactly a period of length (p-1)

96. The least K consecutive odd primes such that the sum of every two of them produces a distinct number

97. Consecutive numbers with the same "sum of prime factors" (SPF)

98. Curio 39

99. Primes p such that R(p) is prime and p^2 = R(R(p)^2)

100. Digital Prime k-tuplets

101. Digital Divisibility Tests

102. Three squares a cube, all primes

103. N=a4+b4 = c4+d4

104. Numbers that are equal to the sum of cubes of its third parts (as strings)

105. a^5 = b1^5+b2^5+...+bn^5

106. Prime-magic squares added up to 2000

107. K Consecutive Smith numbers

108. Methods for generating Smith numbers

109. a1<a2<...<ak such that...

110. Dropping digits primes (by Patrick De Geest)

111. Spoof odd Perfect numbers

112. Automorphic primes

113. Provable primes in Arithmetic progression

114. The Murad's generalization of the Collatz's sequences

115. Prime squares composed by no more than two digits

116. A=B+C, A*B*C is a primorial...

117. Certain p# +1 values

118. Primorial product numbers

119. Sophie-Germain & Twin, chains

120. Primal Squares

121. THE LEGEND OF YANG HUI

122. Consecutive Twin primes

123. Two Frank Rubin's prime puzzles

124. Palindromic, Prime & Sophie-Germain pair of Magic Squares

125. Primes through palindromes

126. Some conspicuous probable primes

127. Non adding prime sequences

128. Sum of consecutive squared primes a square

129. Harshad Numbers

130. The Hexagon of the 19 numbers

131. Growing primes

132. Pascal Primes

133. Pa - Qb = K

134. The 1379-Carrousel-Primes

135. Partitions into distinct primes with maximum product

136. Poor prime strings

137. Product of primes + 1, a square

138. Deletable primes

139. Sdf(x)=p

140. Primes Decades

141. Smarandache Prime Base representation of the natural numbers

142. Optimal Assignation of Primes in several Patterns

143. The first and the last five primes

144. The Langford Prime Numbers

145. The ISPP & SSPP functions

146. Solutions of A2 +X2 = Y2, A = odd

147. Twin & Reversible primes

148. Product of primes - 1, a square

149. Fermat 400

150. Primes type n+/- Fm, for m=0 to 4

151. Euler-Rodríguez set of consecutive primes

152. The Prime Gears Cars Race

153. Espinosa's puzzle

154. Extension and Variation of the GC

155. Follow-up of the puzzle 151

156. One million doors

157. Zip primes

158. Sum of Cubes equal to Square of Sum

159. A follow up to Puzzle 37

160. s(n) and p(n)

161. A Secret Code

162. P² + Q² = p² +q²

163. P+SOD(P)

164. Sequences of Fermatian primes

165. Bye Mr. Suzuki

166. pⁿ -1 =0 mod f(n)

167. Primes m + 2 ^j & m - 2 ^j

168. Primes such that SOD² = POD

169. The unit and the sum of three signed prime-cubes

170. Pseudoprimemania

171. Perfect & Carmichael numbers

172. Minimal Length, prime-complete-rules

173. Ruth-Aaron Triplets

174. Primes & consecutive divisors

175. Integer average & sets of consecutive primes

176. Primes in a circle

177. Primes in a square

178. Shallit Minimal Primes Set

179. Prime Alphametics

180. Primes as a sum of squares

181. (N+k)/k primes

182. Primes with zeros replaced

183. Perhaps a very simple question

184. Gronau's prime triplets

185. Differences between consecutive n^n values

186. Squareful Fibonacci numbers

187. Triangles and Triangular numbers

188. Dividing large numbers

189. Squares and primes in a row

190. A follow up for the puzzle 188

191. P(n)=n(n+1)(n+2)(n+3) - 1

192. Reversible & Digit Complementary Prime Pairs

193. The Andersen's theorem & primes

194. The Palinpoints

195. Primes such that their squares are free of the digit D.

196. Consecutive integers with the same quantity of prime factors

197. Always composite numbers?

198. 2^a - 3^b = c

199. The Prime-Vampire numbers

200. Ones from 1 to p (*)

201. The arithmetic function A(n)

202. The n-th Omega recurrence

203. Perfect primes

204. An old empirical observation

205. Primes is in CI

206. (N-k)/k primes

207. The inventory sequences and the self-inventoried numbers

208. Happy new Year 2003!

209. Triangles of primes

210. Jeff's numbers

211. A beauty limit on prime numbers

212. Substring reversion

213. Hailstone Champion Sequences

214. Trotter's Curio

215. The Ulam Numbers

216 Primes in a square array

217. n in pn

218. Rupinski primes

219. Polignac numbers

220. p - k! primes

221. What are the next?

222. Equations with consecutive primes

223. Consecutive primes and powers of 2

224 Eccentric prime diagonals

225. VIP (Very Sparse Primes)

226. Rolling Primes

227. Research Problem 1.75

228. Sum of twin primes, a square

229. Primes and Hypercubes

230. Primes and a tower of cubes

231. k-Persistent primes

232. Primes and Cubic polynomials

233. A little twist

234. 2003, again

235. Dropping digits primes

236. A Broken Face

237. Alien neighbors

238. The hidden prime

239. psp (2) & n2 -2 numbers

240. Consecutive numbers and consecutive prime factors

241. Highly imperfect primes

242. Sum of distinct squared primes

243. Primes and squares in a square array

244. Null Conjunction

245. As 13

246. The worms

247. Consecutive Smith numbers

248. Find one composite solution

249. From Rudolf to Rodolfo (magic squares and pandigital numbers)

250. Euler, one more time.

256. Jack Brennen old records

257. Primes and sibling numbers

258. Primes and sibling numbers-II

259. Not dividing any pandigital

260. Chains of twins

261. Symmetric prime constellations

262. Semiprimes in arithmetic progression

263. MagicAntiMagic Squares

264. Antimagic Prime Squares

265. Primes embedded

266. Magic rectangles

267. Talisman Squares

268. 23 primes in A.P.

269. 13 primes in A.P.

270. Euclidean questions

271. Prime gap tug of war

272. P(n) & n

273. Consecutive 'good' primes

274. Sierpinski triangles from prime numbers

275. Highly composite polynomials

276. Prime factors of (x^n+y^n)/(x+y)

277. Pi again

278. The Rupinski's question

279. Farideh Firoozbakht asks for the next term

280. 3893257

281. A follow up to Puzzle 24

282. f(p) = f(p')

283. Harshad Left Truncatable numbers

284 A+B=C | A.B.C = pk#

285. μ(2^k-1) mod k

286. Get a simple proof of this

287. Multimagic prime squares

288. Magic squares of (prime) squares

289. Palprimes inside the infinite primes concatenated

290. Primes on Platonic solid faces

291. Primes embedding a given sequence

292. Zigzag Primes

293. Balanced primes

294. How to prove this?

295. Another Alphametic puzzle

296. An intriguing sequence

297. Queens on magic squares

298. Mersene, Mq = (8x)^2 - (3qy)^2

299. Collatz-like sequence of primes

300. UFO message?

301. One million of prime prime residues

302. Primes inside the sequence of primes

303. I'm such a square...

304. A larger square embedded

305. A new version of Puzzle 209

306. Generalized LYM Puzzle

307. Record Smith Numbers

308. AxB = N =A'xB'

309. A property of the prime '5'

310. DPT's on a knight's tour.

311. Sum to a cube

312. Sequence of primes such that...

313. Squares having only k distinct digits

314. (f(n))=prime(n)

315. pn => pn-i + pi

316. Divide a square of primes.

317. Two dimensional constellation of primes

318. 31 = sigma(16) = sigma(25)

319. Approximations to π(n)

320. Dealing with primorials

321. Primes type n^4+4

322. Primeval primes as sum of primeval primes

323. Primes in a Sudoku solution

324. Self-descriptive numbers

325. Zeisel numbers

326. One more Firoozbakht curio sequence

327. Giuga numbers

328. Is this the largest?

329. Odd abundant numbers not divided by 2 or 3.

330. σ(φ(σ(p)))=φ(σ(φ(p)))

331. The prime Russian mountain

332. Odd abundance

333. 'Magic squares' and primes

334. Farideh & the 2004 year.

335. Prime values for σ(n).

336. sigma(n)<prime(n)

337. p inside p2.

338. Domino-Prime-Pyramid

339. Primes & persistence.

340. Resta's approach to Puzzle 337

341. Multiplicative persistence, Erdos style.

342. Primes on a dice.

343. One more Farideh's question

344. Primes in Nature

345. Magic square of cubic primes

346. Happy 2006

347. Properties of numbers that have a Mersenne Number as a factor

348. 414347 prime string

349. 2^d(n) = n + E

350. Primes & primorials

351. E796

352. φ(n!)

353. The first n2 primes in a matrix

354. Another prime game

355. Puzzle 232 in 4th order

356. A minimal set of K primes

357. Consecutive reversible primes

358. Ruth-Aaron pairs revisited

359. First N primes in a circle

360. Complementary divisors to make a prime

361. Multiply, or delete zeros

362. A sequence of primes.

363. A magnanimous company

364. P2 = Q*R

365. P*Q = R*S

366. Three questions about the PGP

367. Two dice to produce prime numbers

368. Attained by invalid arithmetic

369. Approximations to unit adding prime reciprocals.

370. The first 13 numbers

371. A052215

372. Ask Dr. Matrix, prime version

373. Self primes

374. Self numbers

375. Powers which are the sum of initial primes

376. n=p*2^x

377. Add 2 to any digit

378. Sequences embedded in decimal periods of fractions

379. SG primes and its prime average

380. A follow up to Puzzle 42

381. A sequence related to a special case of the Goldbach Conjecture

382. KL(29207), Prime or Composite?

383. Brougnard sequences

384. Prime Reverse Keith numbers

385 Follow up to Puzzle 104

386. CabTaxi, prime version

387. Prime curios in the Pascal's triangle rows?

388. Primes on a dice, again

389. Joe Crump and the search for solutions to 2nmod n=c

390. 493009335

391. 9 dots and 8 lines graph*

392. σ(x) = x+φ(x)

393. A follow up to Puzzle 128

394. No shared digits between composites and its prime factors

395. (2^n+3^n+4^n+5^n+6^n)/2 – 10

401. Magnanimous primes

402. 1263560563

403. 833021343

404. Σ(x^x), for x=1 to n

405. R(38)

406. 1123

407. Prime Multidimensional Arithmetic Progressions

408. First primes embedded in the smallest number

409. Consecutive primes triplets

410. The largest magic square & primes...

411. Magic squares M & p(M)

412. Semimagic square of cubes

413. DPS in AP

414. Prime lucky number triplets

415. Sets of consecutive primes such that...

416. Prime numbers less than 2^18

417. M(e) reversed primes.

418. Honaker's ratio

419. Four SOPF questions

420. Another sequence of primes

421. Staircase of consecutive primes

422. 3N consecutive prime

423. K Consecutive even numbers such that...

424. Empty intervals between consecutive perfect powers

425. Consecutive numbers, increasing quantity of prime factors

426. q = p +rad(p+1)

427. Runs of consecutive numbers such that... (I)

428. Runs of consecutive numbers such that... (II)

429. Consecutive primes & biprimes

430. Grimm's conjecture

431. p = (q/r)3 + (s/t)3

432. A nice pattern with 6 consecutive primes

433. Three consecutive integers

434. σ(σ(x)) = σ(x)+x

435. φ(x) + σ(x) = k.x

436. 43 =4^2+3^3

437. A special set of binary numbers

438. 1024383257

439. Fibonacci Primes Puzzle

440. σ(n)=2n-1

441. σ(n)+π(n)=k.n

442. Primes ending in 9

443. Sum of cubes of consecutive primes

444. Pseudo twin primes

445. Consecutive integers with prime SPF

446. S(p, q)=p.q

447. Zeros on p.q

448. p+q not divided by 3

449. Count N composites after p

450. K extended factors for sum of two consecutive primes

451. Prime factors of n, φ(n) & σ(n)

452. (a^2)!+2^(a^2) = b*(1+a^2)

453. DPFP

454. Number of primes of the form n^2 + 1

455. 1+σ₀(n).σ(n) = n*rad(n)

456. Mersenne Primes as a sum of consecutive primes

457. Prime word embedded

458. Related to Puzzle 451

459. Related to Puzzle 457

460. Sqrt[p(x)*p(x+y)-1]= y

461. Consecutive squares + prime = prime.

462. p+q+r=3*q

463. k.P(k)+(k+1).P(k+1)

464. p+4.x²

465. Factorials

466. phi(n-1)=phi(n)=phi(n+1)

467. Primes in the last two digits

468. Primes & Semiprimes Gaps

469. 5040

470. p+2=semiprime

471. n and n^2 use only prime digits

472. What is the second solution?

473. N = n^p + p^n

474. Two last puzzles for this 2008

475. A question related to ABC Conjecture

476. A question related to Collatz Sequence

477. Sum of k primes = Product of k integers

478. Factorials as sums of consecutive prime

479. P+1 & P+1+S are primes

480. Primes on an Dodecahedron

481. E.E-p=q

482. Two Bergot questions

483. p^2=a^2&b^2

484. ABC conjecture and consecutive primes

485. Farideh's guess

486. Reserved for the Gods?

487. Follow up to Puzzle 485

488. Follow up to Puzzle 487

489. Mersenne Primes & 0, 23 & 1535

490. 2^n-2^k+1, a square

491. Sum of any combination is not prime

492. 59 and still counting...

493. p^p = x*a^2 + y*b^2

494. f(n)=product(prime(di))

495. P*R(P)+1 = Prime

496. P*R(P)+1 = Palprime

497. Sqrt[p^2+q^2- 9]

498. p*s+q*r is never a square

499. 6*7*8*9 - 1 is prime

500. 211896

501. Three Consecutive primes a prime

502. Adding consecutive 2n+1 primes a prime

503. phi(x)*sigma(x) = x^2 - (1/n)*x

504. F(n) & G(n)

505. P(m^2 + 1) = n^2 + 1

506. Reversible primes again

507. phi puzzle from Farideh

508. phi(n)=phi(n+1)

509. S(n+1):=S(n)^2 - 2

510. nrp(2^m) = m + 2

511. Primes reversing N, N^2, & N^3, ..., N^K

512. b^c=a(mod d)

513. Four consecutive primes

514. S(pi)= q mod r

515. Phi(Phi(x))

516. Fifty nine years old

517. φ(x) + σ(x+1) = 3x

518. Pi=prime(Pi-1)

519. Triangles with prime sides

520. Prime divides Repunits

521. p^p=p mod(q)

522. Three sets of k consecutive primes

523. Increasing residues

524. x = 1 (mod phi(x))

525. D= d1*P1 + d2*P2 +...dn*Pn

526. p2^2-p1^2 = n!

527. sigma(x) = 1 (mod x)

528. Prime quadratic residues

529. The prime-explosion Bergot graph

530. Twins pointing to equidistant trios

531. Two products of consecutive primes a power

532. Puzzle 529 re-loaded: sizing the prime nebulas.

533. phi(sigma(n^2)) = n(n+1)

534. The sum of any two terms a prime or...

535. The minimal seed Xo/Yo for square roots

536. Primes in several bases (again)

537. n^n = n mod [prime(n)]

538. (3n^2+3n+1) ^2 | (3n+1)^(3n+2) + 3n+2

539. n consecutive primes same residue modulo 4

540. b^(2^n)+c

541.- Emirps again

542.- Sigma (x)=q^n

543.- Primes as sum of powered consecutive primes

544.- Yet another prime Prime Race

545.- 14 or 17<->25

546.- Non-Pandigital primes

547.- A064507

548.- dr(p*n) = dr(n)

549.- Better than 210

550.- Consecutive primes producing semiprimes

551.- Three nines & repunits

552.- p=k mod [prime(k)]

553.- SCN=PCP

554. P+10^n

555.- q=p(i) mod [p(i+1)]

556.- Follow up to Puzzle 554

557.- H(m, a)

558.- Goldbach decomposition & consecutive primes

559.- Mauldin / Tijdeman-Zagier Conjecture

560.- Same quantity of prime factors

561.- Square of consecutive prime & even numbers

562.- Heleen's sequence

563.- P=a^2+b^3

564.- Primorials & primes

565.- [(d)n] mod d^n = k

566.- Semiprimes in a given interval

567.- p1+...+pk = q1*...*qk

568.- SOPF(N)=SOPF(RN)

569.- Prime-Magic Hexagon

570.- Does this happen again?

571.- P(a)=P(b) mod(P(c)

572.- (P+Q)@3<>0

573.- Primes & its digital roots

574.- P.Q composed by only two distinct digits

575.- Primes | k leftmost digits are divided by p(k)

576.- Triangular Magic Triangles

577.- Happy prime Valentine day!

578.- The smallest prime concatenating the first k primes

579.- A triangular array with primes

580. An equivalence for twin primes

581. 142857

582. p.q=c^2+1

583. Traveling intertwined primes

584. Embedded but not overlapped prime factors

585. 37677869739

586. The best number is 73

587. Concatenating absolute differences

588. Squares sharing no one single digit

589. Palindromes multiplying consecutive primes

590. P-1 & P+1 with the same quantity of prime factors.

591. 1304119699

592. p.(p-1)=q&(q+1)

593. Primes by transportation

594. 999997600699

595. p*q -> p^2 + p*q + q^2

596. 12*n*(n+2)+1

597. A follow up to Puzzle 596

598. A18781

599. Weird numbers

600. Follow up to Puzzle 599

601. Pair of primes (p, q) such that...

602. T(73)=37*73

603. p=(q*r+s)/2

604. Primes in 2&3&4&...&n

605. Follow up to Puzzle 604

606. Puzzle 738 from Claudio Meller's site

607. A zeroless Prime power

608. 2^(2^n)+k

609. Rectangling the square.

610. Rectangling the square-II.

611. Puzzle 2-3-5-7.

612. Prime-Doublets.

613. Curio sum of primes.

614. Always composite by insertion

615. Abs[R(n/3)-n]<=1

616. Primes by dupplicating some digit

617. Concatenating & superposing

618. GCD(1+P, S)

619. Odd midpoints

620. 2012

621. Puzzle 411 revisited

622. Primes as concatenation of two squares

623. p^2+3pq+q^2=r^2

624. Nice integer quotients

625. Sum of squares of prime divisors

626. Frank Rubin, kissing primes

627. Nested Carmichael numbers

628. Fermat Pseudoprimes

629. Non-primitive Carmichael numbers

630. Gap between p(n-1) & p(n+1)

631. Follow up to Puzzle 630

632. [R(n)+1]@n=0

633. Palindromes & Pandigitals

634. Primes in Collatz trajectory

635. 34155

636. Primorial as product of palindromes

637. Factorials as product of palindromes

638. Special integer quotients

639. Sigma (n+12m) = Sigma(n)+12m

640. A sequence of semiprimes.

641. Cunningham Chains of semiprimes.

642. N=A&B=A+B^3

643. 134757431

644. 123 Curio

645. Generalized Dudeney Numbers

646. Curio 364

647. Shifted alphabet rows

648. P^2 = A^2&B^2

649. An algorithm for this conjecture

650 Triangular, Primes & Powers of 2

651 6866683

652 Recursively P_i+1= POD(P_i) + 1

653 R(p) is n^n.

654 Factors for p(n)#+/-1

655 pq+rs, perfect square.

656 Primes using certain quantity of digits

657 Look and say sequence

658 Find primes such that...

659 Sandwiched palindromes

660 Exotic primes

661 Carpet palindrome Persian art style

662 547716131821

663 Pandiagonal prime magic squares

664 The queen covering the chessboard

665 (p+q)*(q+r)=m^n

666 Columns = Rows

667 Puzzle 77

668 Fortyfive

669 2013 and 2014

670 The same sum of divisors

671 Most Perfect Magic Squares

672 sigma(sigma(x)) + sigma(x) = 3x

673 Sudoku & primes, again

674 Concatenating the squares of consecutive primes

675 p = -1+2^57885161

676 primes in a row such that...

677 primes in a row such that... II

678 Find the least vector of integers such that...

679 Prime-proof odd integers

680 The largest palindrome prime-proof odd integer race

681 Stanley Antimagic Squares

682 Stanley Antimagic Squares-II

683 Rubin's puzzle

684 Primes in N dice

685 Follow up to puzzle 683

686 Filling the grid (Le Monde puzzle)

687 17769643

688 Follow up to Puzzle 687

689 Pandiagonal and twin primes

690 Unreachable primes

691 Conjectures related to Gilbreath's scheme

692 Consecutive prime gaps biprimes

693 Prime Chemical Compounds

694 S(p,q)=p&q

695 Pandiagonal & twin primes

696 1801

697 Puzzle 105, revisited

698 Others as 129

699 Special prime pandigital magic squares

700 p & q primes such that ...

701 Alphametic magic square

702 Adding emirps to a cube

703 Dividing a set of primes in other two

704 Find a prime such that...

705 2213

706 Palindromes generating palindromes

707 The smallest sum for a set...

708 Find sets of k consecutive primes such that...

709 Primes P=A&B such that...

710 6252893229398 & non-semiprimes

711 Composites with the exactly the same digits than its prime factors

712 Primes or squares

713 Primes between perfect powers

714 Composites that remain composites when...

715 phi(x + n) = sigma(x - n)

716 Problem 9 of...

717 Associative squares Stanley

718 A follow up to Puzzle 700

719 Extension to Ruth Aaron pairs

720 x^2&y^2 or y^2&x^2 squares

721 p(i)= DR(p(i-1))&(p(i-1)\10)

722 2^m-1 consecutive integers having m prime factors

723. Pandiagonal magic squares of consecutive primes

724. Extending the OEIS sequence A229908

725. The ABA numbers

726. Completing the OEIS sequence A235031

727. Extending the OEIS sequence A235680

728. Consecutive Moran numbers (extending the OEIS sequence A235397)

729. Consecutive Hoax numbers (extending the OEIS sequence A235766)

730. Trio of Consecutive Achilles numbers

731. Stanley Antimagic squares of consecutive primes

732. Sum of cubes a square

733. Integers equal to the sum of the squares of their prime divisors.

734. "Common Sigma, Uncommon Clique" Numbers

735. Consecutive primes such that the sum of their digits generates another set of consecutive primes.

736. Associative Stanley squares of consecutive primes

737. Maximize log(s) / log(maxPrimeFactor(s))

738. Special Cunningham Chains

739. Carmichael numbers of special form

740. Misprinted product, find the correct one

741. Find the smallest set of distinct primes such that...

742. Prime-Golygons

743. The least largest prime in a 4x4 magic square

744. The smallest prime such that...

745. A number 20 digits large, best qualified

746. A follow up to Puzzle 742 (about golygons)

747. A second follow up to Puzzle 742 (about golygons)

748. A third follow up to Puzzle 747 (about 3D-golygons)

749. Prime magic cubes

750. A special 5x5 prime magic square

751. Named primes producing primes

752. Palindromes as sum of the first k primes

753. Prime lattices

754. Quantity of primes in P+Q

755. Upside Down Magic Squares

756. Primonacci

757. Follow-up to Puzzle 756

758. Associative magic cubes of prime numbers

759. Palindrome primes in A.P.

760. A087711

761. On certain consecutive primes p & q

762. Conjecture from Ribenboim's book

763. P(n) = P(n)^P(n+1) mod (P(n)+P(n+1))

764. N integers in a row such that...

765. p^a = q^b + r^c.s^d

766. A Follow up to Puzzle 764.

767. A second Follow up to Puzzle 764.

768. Primes as m sums of triangular numbers.

769. Magic squares and consecutive twin primes.

770. Eygptian Fraction Magic Square

771. First P primes in a square.

772. Entry 1363 by Claudio Meller

773. Necklaces with k primes

774. S(i) and Rad(i)

775. Triangles and consecutive primes

776. Ten consecutive integers such that...

777. Ultra magic squares

778. A follow-up to Puzzle 774

779. A first follow-up to Puzzle 776

780. A second follow-up to Puzzle 776

781. A second follow-up to Puzzle 776

782. Prime-Generating non-polynomials

783. A sequence of composite integers

784. Find some more solutions

785. Extend this table

786. Looking for certain set of integers.

787. Fibonacci as sum of two consecutive primes.

788. P&p(i)^2&RP

789. Almost primes Fibonacci numbers.

790. Prime Langford pairing

791. Inserting consecutive primes

792. Prime numbers equal quantity of digits...

793. Entry 1399 from Claudio Meller's site

794. Prime Generalized Palindromes

795. Primes reversing substrings

796. Looking for certain palprimes

797. Primes and perfect numbers related

798. A nice puzzle by Kamenetski.

799. Follow-up to Puzzle 798.

800. A nice numbers sequence.

801. A nice stepladder of primes

802. A follow up to Puzzle 801

803. Panprimmatics

804. Palindromes and primes

805. Prime gaps containing...

806. Extended n-Parasitic numbers

807. Symmetrical compositions of twin primes

808. Palprimes that remain...

809. Two linked Goldbach prime-stairs

810. Sum of consecutive triangulars and primes

811. Primes and Sum of consecutive triangulars-II

812. Other chains of primes

813. Symmetrical compositions of consecutive twin primes

814. Primes and squares such that...

815. Another prime pine

816.Primes between n*k and n*(k+1)

817. 2016 and prime numbers

818. A follow up to Puzzle 814

819. A follow up to Puzzle 314

820. The Sunduram's sieve

821. Prime numbers and complementary sequences

822. About OEIS sequence A193890

823. String of digits 1379 full of primes

824. Insecure numbers

825. Primes type Liouville

826. Primes and Pascal Triangle

827. A sieve for twin primes

828. A sequence of primes such that... are free of the digits 2,0,1,

829. Dividing the first k prime to obtain new primes.

830. Entry 1439 from Claudio Meller's site.

831. Rings of primes.

832. Follow-up to Puzzle 828.

833. A special set of integers.

834. A274071.

835. Goldbach squares.

836. Bills serial numbers.

837. Kaprekar prime numbers

838. Follow up to Puzzle 833.

839. Follow up to Puzzle 835.

840. Second follow up to Puzzle 835.

841. Symmetrical compositions of consecutive pairs of cousin primes

842. Multiple or divisor

843. Looking for more Kaprekar prime numbers

844. Primes inside Sudoku solutions

845. 31 consecutive integers with an even quantity of prime factors

846. A follow up to Puzzle 844

847. Consecutive primes with the same Collatz length.

848. p(0)_nq is prime for n=0,1,2,...k

849. 9x9 Magical square and pandigitals.

850. The wagon prime.

851. Puzzle 827 revisited

852. Primes and convolution

853. The Euler polynomial again

854. Follow up to Puzzle 853

855. Second follow up to Puzzle 853

856. Cascade of primes 4k+1

857. A second cascade of primes 4k+1.

858. Updating the Puzzle 203.

859. A follow-up to Puzzle 203.

860. Primes of the Mersene primes reversed.

861. Puzzle 1467, by Claudio Meller

862. Redo Puzzle 861

863. 2017 a new prime year

864. 10958, the only hole...

865. Area Magic Squares

867. Follow up to Puzzle 833

868. Magic squares 3x3 and palprimes

869. Prime nested magic squares

870. Prime nested magic squares-II

871. Claudio Meller 1476

872. Integers (p^2)*Q

873. Follow-up to Puzzle 871

874.Consecutive integers with increasing or non decreasing quantity of divisors

875.Vector of primes that generates distinct primes

876.Prime Tuples

877. Integers represented using the minimal first consecutive primes...

878. Consecutive abundant integers

879. More about Q3 from Puzzle 876

880. Consecutive odd abundant integers

881. 123456789 and prime numbers.

882. Prime sequence type A(Z)_iB

883. Large three consecutive semiprimes

884. Almost consecutive integers type k-almost primes

885. Square-free almost consecutive integers type k-almost primes

886. The earliest largest set of consecutive integers type k-almost primes

887. p(n)^c-2 is prime

888. Prime-Squares

889. Prime-Squares-II

890. Magic Squares and Pythagorean Triplets

891. The first N integers arranged to form a Palindrome

892. Primes as a concatenation of a series of powers of a prime

893. Primes as a concatenation of a series of powers of 3, with 6m

894. The first N integers X type arranged to form a Palindrome

895. K consecutive quartets of consecutive primes with different ending digit

896. Optimal packing of a set of integers

897. Integers as sum of special Egyptian fractions.

898. Given a square filled of integres, get...

899. A follow-up to Puzzle 899

900. Why 25

901. A question about consecutive integers

902. two vectors of consecutive primes such that...

903. Follow-up to Puzzle 902

904. Follow-up to Puzzles 902 & 903

905. Primes generated by a recursive formula?

906. 2018

907. 10|p(n)^2 + p(n+1)^2

908. Descending residues

909. Palindrome Friedman prime numbers

910. Follow up to Puzzle 908

911. Follow up to Puzzle 910

912. Two successive primes and oblong numbers.

913. The last two digits of a prime is a prime.

914. Puzzle 172, revisited.

915. Follow-up to Puzzles 172 & 914

916. Follow-up to Puzzle 58

917. Q=P+A*B

918. Primes on the line y=x

919. K csc primes without certain ending digit

920. An enigma related to A291582

921. Follow-up to Puzzle 920

922. Follow up to Puzzle 634

923. 2*P+Q is prime

924. Follow up to Puzzle 923

925. Seven primes associated (Puzzle 348 revisited)

926. pandigital and prime numbers

927. Prime solutions to HTP

928. Surreal integers

929. Six primes such that the sum of any five is a prime number

930. Follow up to Puzzle 791

931. Twin primes 4x4 magic square.

932. A puzzle about emirps.

933. p inside p^3.

934. The prime 7499

935. pi+SOD(pi)=p(i+n)

936. Palprimes such that...

937. A non-composite sequence?

938. The Soothsayer sequence

939. Numbers in Arithmetical progression whose sum of divisors is same (CYF 35)

940. Digits on p^k

941. nxtprime(p) inside p^2

942. Semiprimes and Pascal Triangle

943. Primes that remain prime when...

944. Palprimes generating palprimes

945. Modular generation of primes from a prime.

946. The largest prime that divides...

947. Circulant Matrixes and a sequence of primes

948. Vampire numbers again

949. Another Collatz-like sequence

950. Bi-truncatable primes

951. Mersenne primes as self-numbers.

952. Consecutive self primes

953. Q2 from Puzzle 658.

954. Growing by the center, sequence of primes

955. Variation of Puzzle 954

956. A trio of integers and six squares

957. Largest prime with pandigital ordered expressions

958. P^3 has K tri-prime-partitions.

959. Integers equal to, both, the sum of...

960. Redo Puzzle 793

961. Redo Puzzle 960

962. Claudio Meller 1519 entry.

963. Minimal quantity of Prime Arithmetic Progressions to...

964. A308357

965. Partitioning an 8x8 square

966. Update Puzzle 353.

967. Extending Puzzle 485.

968. Another property of primes 4m+1.

969. Rad(m - 1) = Rad(phi(m))

970. A309566

971. The cube of N such that...

972. Three questions about Primevals

973. Largest known twin & emirp

974. More twins like these...

975. p repeated p times.

976. m/d+/-d primes.

977. A special set of primes.

978. Improve this curio

979. Primes and sum of repunits

980. The "Commas" sequence.

981. Redo Puzzle 957 for titanic prime solutions

982. Home primes second class

983. Happy New Year 2020

984. Happy new year 2020-II.

985. Consecutive primes paired to consecutive powers of 2.

986. Consecutive primes from a given set of integers.

987. Another puzzle related to the year 2020

988. Another puzzle about factorials

989. Smallest integer that generate at least n different primes

990. K n-values in AP with the same sigma(n)

991. Peculiar n-gons

992. primes on the faces of a dice

993. Follow-up to Puzzle 992

994. A puzzle for quarantine days.

995. Another sequence of primes

996. A variation of Puzzle 986

997. m - n + s - Floor[m*s/n]=1

998. A306431

999. In Memoriam to John Horton Conway *

1000. Prove that math is fun

1001. Anti-divisors of prime numbers

1002. Consecutive primes that are also happy numbers

1003. Right Perfect Primes

1004. Sum of all the first primes 4k+3 as perfect squares

1005. Palprimes from prime factors of consecutive integers

1006. Bemirps as index of the π(i), the prime counting function.

1007. Self inserted primes

1008. Another curio by G.L. Honaker, Jr.

1009. The tallest pyramid of Emirps

1010. 21 is a Fibonacci number special...

1011. Primes altering any digit of an integer

1012. Primes on the skin of Fibonacci's

1013. Primes as subsequences in pi

1014. Observation about three consecutive primes

1015. Sequence of semprimes

1016. Vector of primes such that...

1017. Sum of reciprocal of primes such that...

1018. Follow-up to Puzzle 1016

1019. Follow-up to Puzzle 625

1020. Follow-up to Puzzle 899

1021. p(k)+p(k+1)+1

1022. x(n)=(n - 1)^n + n

1023. Another ladder of primes...

1024. Primes from primes

1025. 352757

1026. Another pine-like-prime puzzle

1027. Integers as sum of repdigits

1028. Prime Generating Modular functions

1029. p that divides the number of partitions of p

1030. A puzzle cousin of Puzzle 1027

1031. Rigidly-deletable primes again

1032. Integers EOM

1033. Primes p+2^q

1034. P+6k=Q, etc

1035. tau(sigma(x)) * sigma(tau(x))

1036. P + R(p) such that...

1037. (m,n) producing five twin primes.

1038. Three puzzles about consecutive primes.

1039. k-number of prime divisors obtained by substitution of...

1040. Pair of consecutive even integers such that...

1041. σ₂(x)=σ₂(x+1)

1042. Another puzzle about emirps

1043. Another puzzle about Keith numbers

1044. Sequence of primes concatenating primes...

1045. One nice puzzle from Paolo Lava

1046. Reversed binary are decimal twin primes

1047. p*2^p+1

1048. Follow up to Puzzle 486

1049. p=sum of (di^di)

1050. A follow-up to Puzzle 1049

1051. About consecutive integers whose reverse are primes.

1052. Pythagorean triplets such that...

1053. p=concat(a,b) such that...

1054. q=concat(x,y)

1055. Google Prime Number

1056 Follow-up to Puzzle 1055

1057 A cycle of ten primes

1058 Alike the puzzle 1057

1059 Set of consecutive primes such that...

1060 Can you find more solutions?

1061 Consecutive numbers and the quantity of distinct prime factors

1062 Consecutive numbers and the quantity of distinct prime factors-II

1063 A subset of A289351

1064 GCD(2^p+1,3^p+1)

1065 A larger integer than 45 such that...

1066 4 consecutive triangular and sphenic numbers

1067 Primes in a square such that...

1068 Follow up to Puzzle 1067

1069 Follow up to Puzzle 1066

1070 Happy Holidays puzzle with atomic numbers

1071 Follow-up to Puzzle 1070

1072 Exactly k consecutive odd numbers with ...

1073 p*q=1+k^2

1074 Semiprimes stairs

1075 A conjecture about twin primes

1076 Set of integers N, 1<N<S such that...

1077 These numbers that are...

1078 Find the next prime of the form...

1079 Forest of prime numbers

1080 sigma3(x) = y

1081 2*7*13-3*5*11=17

1082 Chain of primes such that...

1083 A046883

1084 Chains related to twin prmes

1085 A follow-up to Puzzle 1079

Puzzle 1086 Take the representation of a prime p in the bases from 2 to 9, and...

1087 (p^2-1)/24=q...

1088 p = x U y such that p = x^a + y^b

1089 17=2^3 + 3^2

1090 Numbers that are the sum of k, k+2, ... consecutive primes

1091 Another stair of primes

1092 Consecutive integers of the same parity

1093 Sum[Round[Sqrt[k]],{k,1,n}]

1094 Concatenated Digit Count as Prime Factor

1095 RPP(74207281)

1096 37 & 73 coming from 10

1097 Modular non-polynomial prime generators

1098 A Follow-up to puzzle 265

1099 A Follow-up to puzzles 782 and 1097

1100 Another function to produce only and all the primes?

1101 Primes p that divide the concatenation of sigma(p-1) and sigma(p+1)

1102 Consecutive primes ending in the same digit

1103 successive primes p+10^n

1104 Sum of powers of primitive roots

1105 A variation related to Puzzle 1103

1106 pkcp mod (skcp) = p

1107 Place 11 after its base result

1108 Integers equal to its sum of nonprime proper divisors.

1109 Related to A112386

1110 Triplets of consecutive primes

1111 Quadruplets of consecutive primes

1112 Concatenation of prime expansion in different bases

1113 A pair of Diophantine equations.

1114 Consecutive integers such that...

1115 Follow up to Puzzle 1114...

1116 A358527

1117 2023

1118 Prime[n] + k*(Prime[n + 1] - Prime[n])

1119 Consecutive primes as 11 & 13

1120 F(n) = 2^n - A(n)

1121 Phi(p)/Phi(p-2)=2

1122 OEIS A005385

1123 Tetractys

1124 Pentactys

1125 About Feb 28

1126 518!!

1127 Prime(11!)+Prime(11)!

1128 Prime(n)!-Prime(n!)

1129 OEIS A137990

1130 As 68

1131 TEST FOR FERMAT'S PSEUDOPRIMES TO BASE 10

1132 The largest row of K distinct primes such that...

1133 Get another proof

1134 F(n)=|(2^n-1)/(2n+1)|

1135 Polynomial with consecutive primes such that...

1136 Divisors functions and Fermat primes

1137 Consecutive primes & n#

1138 A068192

1139 Prime producing IRREGULAR polynomials

1140 Test for Sophie Germain primes

1141 Closed Magic Knight tours 12x12

1142 p(n+1) = floor[p(n)#*k - p(n)*floor(p(n-1)#k-1)]; P(1)=2, k=2.920050977316134...

1143 Palindromic Prime Pyramid step 3

1144 Queen attacking primes over a Knight tour 8x8 Matrix.

1145 Divisors of Fermat numbers.

1146 Picking out matches.

1147 Successive prime using the functions....

1148 Pyramids of palprimes such that...

1149 A110588 vs 033949

1150 Find the following numbers...

1151 Follow-up to Puzzle 1150

1152 7107379973

1153 a new sequence...

1154 Consecutive primes over a replacement system

1155 Equilateral triangle with an interior point such that...

1156 1738967

1157 Interesting formulas?

1158 A unique polydivisible integer

1159 Similar to Puzzle 48

1160 A Puzzle related to 2024

1161 8757193191

1162 n*2^(2n + 1) + 1

1163 Palindromic primes that are semiprimes when turned upside down.

1164 181601808106181

1165 Two puzzles from Mr. N. Nomoto

1166 Two puzzles from Mr. N. Nomoto-II

1167 n!+239

1168 Primes for the Baxter-Hickerson function

1169 A follow-up to Puzzle 782?

1170 Perfect numbers and Ore´s harmonic numbers

1171 Delete power and sum

1172 Follow up to Puzzle 1171

1173 F(p)=(p^2+1)/2 with p prime

1174 Twin Prime sums between Twin Primes

1175 A variation of A322743

1176 ((((n-1)!)^2+4*n-1))/(n*(2n-1))

1177 Golden Ratio Primes

1178 F[n] = Floor[(Prime[n] + 1)^2/(Prime[n + 1] - 1)]

1179 A sequence by Polo Lava

1180 A puzzle by V. F. Izquierdo

1181 A puzzle by S. M. Ruiz

1182 Another sequence by Paolo Lava

1183 F(n)=(Floor(n!/E) + Mod(n, 2))/n

1184 Floor[n GoldenRatio] =n+ Floor[n/GoldenRatio] for all n=>1

1185 4940867.

1186 A puzzle from Emmanuel Vantieghem.

1187 PrimePi[(Prime[n + 1]^2 + Prime[n]^2)/(Prime[n + 1] + Prime[n])]=n

1188 Sum of product of primes step 2

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