Problems & Puzzles:
Problems
1.- David
Silverman Question 
2.- Carl
Pomerance Observation
3.- Erdos
Conjecture
4.- Fortune
Conjecture
5.- Missed
prime factors in Woodall numbers
6.- Primes
and Partitions
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
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
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)
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.
67.
Multigrade Prime Solutions.
68. More on
Brier numbers.
69. More on
Brier numbers-II.
70. Set of
integers whose sum of any two is a perfect square
71. n & pi(n)
such that...
72.
Consecutive primes inside a 9x9 square such that...
73.
Minimal symmetric tuples from consecutive
twin primes...
74.
Prime Number Polyomino Islands in Consecutive-Odd-Number-Labeled
Hilbert Curves
75.
The Castillo Toloza, Prime Counting Function,
Q(x)
76.
More on Egyptian fractions
77.
Accumulating primes in a 2-pans balance (A332788)
78.
a(10) in A177892
79.
More on Egyptian fractions-II
80.
Twin primes generating consecutive...
81.
Pythagorean triangles with triangular sides
82.
Pythagorean triangles again -II
83.
Follow-up to Puzzle 178
84.
Follow-up to problem 67
85.
Follow-up to puzzles 18 and 31
86.
A smaller Sierpinski integer
divided by 3
87.
More questions about Brier
integers
88.
Follow-up to problem 63
89.
Palindromic binary
expression of primes squared
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