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
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