Question

Getting factors of Mersenne numbers. Why does $2^p-1|2^b-1$ where $p|b$ and $p$ is prime and $b\in Z$?

score 35 · Answer 1 · 2026-02-23 03:00:02

35

Views

Getting factors of Mersenne numbers. Why does $2^p-1|2^b-1$ where $p|b$ and $p$ is prime and $b\in Z$?

Published on 23 Feb 2026 - 3:00

score 106 · Answer 2 · 2026-02-23 02:59:20

106

Views

Can it be shown that numbers of a certain form produce primes more often than expected?

Published on 23 Feb 2026 - 2:59

score 221 · Answer 3 · 2026-02-23 02:55:25

221

Views

Question about the exponents n in Mersenne Primes.

Published on 23 Feb 2026 - 2:55

score 429 · Answer 4 · 2026-02-23 02:58:30

429

Views

About how much time would it take to test the primality of a billion digit Mersenne number with a typical processor?

Published on 23 Feb 2026 - 2:58

score 212 · Answer 5 · 2026-02-23 02:56:53

212

Views

Property of some composite Mersenne numbers

Published on 23 Feb 2026 - 2:56

score 87 · Answer 6 · 2026-02-23 02:59:30

87

Views

There exists infinitely many primes formed of 2^(F[n!+1])-1

Published on 23 Feb 2026 - 2:59

score 80 · Answer 7 · 2026-02-23 03:00:57

80

Views

About the probability that the number of Fermat primes is infinite.

Published on 23 Feb 2026 - 3:00

score 65 · Answer 8 · 2026-02-23 02:58:27

65

Views

Let $x=2^{p-1}-1$ be composite, $p$ prime and $3\mid x$. Why $p \mid x$?

Published on 23 Feb 2026 - 2:58

score 150 · Answer 9 · 2026-02-23 03:01:18

150

Views

Prove that number of times $3$ divides $2^n\pm1$ is exactly one more than the number of times $3$ divides $n$

Published on 23 Feb 2026 - 3:01

score 76 · Answer 10 · 2026-02-23 02:57:41

76

Views

Odd perfect numbers having as prime factors exclusively Mersenne primes and Fermat primes: reference request or proposal as an exercise

Published on 23 Feb 2026 - 2:57

score 158 · Answer 11 · 2026-02-23 02:56:01

158

Views

Show that $M_p^p\equiv 1 \mod p^2$

Published on 23 Feb 2026 - 2:56

score 271 · Answer 12 · 2026-02-23 03:00:04

271

Views

On the equation $\psi(-1+2(\psi(n)-n))=n$ involving the Dedekind psi function, as a characterization of Mersenne primes

Published on 23 Feb 2026 - 3:00

score 1.5k · Answer 13 · 2026-04-01 18:44:49

1.5k

Views

Prove that $2^{13}-1$ is prime

Published on 01 Apr 2026 - 18:44

score 169 · Answer 14 · 2026-02-23 02:56:02

169

Views

Density of extended Mersenne numbers?

Published on 23 Feb 2026 - 2:56

score 268 · Answer 15 · 2026-04-03 21:23:23

268

Views

Lucas-Lehmer test for Mersenne and Wagstaff numbers?

Published on 03 Apr 2026 - 21:23

List Question

Getting factors of Mersenne numbers. Why does $2^p-1|2^b-1$ where $p|b$ and $p$ is prime and $b\in Z$?

Can it be shown that numbers of a certain form produce primes more often than expected?

Question about the exponents n in Mersenne Primes.

About how much time would it take to test the primality of a billion digit Mersenne number with a typical processor?

Property of some composite Mersenne numbers

There exists infinitely many primes formed of 2^(F[n!+1])-1

About the probability that the number of Fermat primes is infinite.

Let $x=2^{p-1}-1$ be composite, $p$ prime and $3\mid x$. Why $p \mid x$?

Prove that number of times $3$ divides $2^n\pm1$ is exactly one more than the number of times $3$ divides $n$

Odd perfect numbers having as prime factors exclusively Mersenne primes and Fermat primes: reference request or proposal as an exercise

Show that $M_p^p\equiv 1 \mod p^2$

On the equation $\psi(-1+2(\psi(n)-n))=n$ involving the Dedekind psi function, as a characterization of Mersenne primes

Prove that $2^{13}-1$ is prime

Density of extended Mersenne numbers?

Lucas-Lehmer test for Mersenne and Wagstaff numbers?

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