Problems & Puzzles: Problems

1.- David Silverman Question solution.gif (285 bytes) 

2.- Carl Pomerance Observation 

3.- Erdos Conjecture 

4.- Fortune Conjecture 

5.- Missed prime factors in Woodall numbers 

6.- Primes and Partitions solution.gif (285 bytes)

7.- Primes and Parity of x and its inverse x’, module p 

8.-(m, n+1) and (m+1, n) with the same set of prime factors

9.-Let f(n) be the number of ways of representing n solution.gif (285 bytes)

10.-Find a 500-digit prime p and positive integers x, y

11.-Here you are asked to find primes of the following form (pr - 1)/(pd -1), expressible in more than one way.

12.-Prime producing polynomials  

13.-The Gap of the Beast solution.gif (285 bytes)

14.-N and N^2-1 powerful numbers 

15.-Why the Twin Constant is so close to 2/3?

16.-A ‘little puzzle’ from Mike Keith (12/12/98) solution.gif (285 bytes)

17.-The largest known sequence of consecutive and reversible primes.

18.- Pi as a concatenation of the smallest contiguous different primes

19.- Divisors (I): The least number N(d) with d number of divisors.

20.- Divisors (II): K consecutive numbers with the same number of divisors.

21.- Divisors (III). Certain questions about s(N), the sum of divisors of a number N.

22.- Divisors (IV) Aliquot sequences, factorizing s1131 (276)

23.- Divisors (V) Aliquot sequences, Sociable Numbers.  

24.- Carmichael Numbers 

25.- The William Paulsen's Prime Numbers Maze  

26.- The earliest Cunningham Chains.  

27.- Congruent K contiguous products of consecutive numbers.  

28.- K least consecutive numbers n such that are not squarefree 

29.- Brier Numbers  

30.- A stepladder to Ba sequence

31.- Fibonacci all composites sequence

32.- Fibonacci and permuted all composites sequences 

33.- The extreme prime triplets

34.- Proving & hiding

35.- More wrong turns...  

36.The Liskovets-Gallot numbers  

37. The Liu Fengsui's Prime Formula

38.  Sebastián Martín Ruiz Prime formulas

39.  The primes sequence and the Sebastian's function

40.  Crump's equation

41 . Iso-Omega Integers

42 . Floor Exponent Prime Sequences

43 . Catalan Numbers  

44 . Twin-primes producing polynomials race

45 . A follow up to Problem 8

46 . Holes and Crowds-I

47 . Holes and Crowds-II

48.  Prime Simple Perfect Squared Rectangles  

49.  Sierpinski-like numbers

50.  Is there a Cullen prime Cn with n prime ?

51.  A kind of prime fractions

52.  ±p ± 2^n

53.  Powerful numbers revisited

54.  AP22 with the difference 43#

55.  Fibonacci dividing terms

56.  p1*p2*…*pk = q1+q2+…+qk

57.  Carmichael numbers c & 2c+1

58.  Brier numbers revisited

59.  Wieferich-non-Wilson primes

60.  Symmetric primes on each side.

61. Problem 20 revisited

62. Symmetric k-tuples of consecutive primes

63. 3x3 Magic squares composed by triangular numbers.

64. Prime convex quadrilateral

65. Prime convex polygons

66. Every positive is integer is the sum of 3 palindromes. Looking for another proof.

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