List questions from mersenne-numbers

Published on 28 Jul 2018 - 22:27

86

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When $q$ is prime and a Wieferich prime $p$ divides $\ M=2^q-1\ $ . Why can we conclude $\ p^2\mid M\ $?

Published on 22 Aug 2018 - 7:27

190

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$b^{n}+1$ is prime only if $b\equiv0\pmod2$ and $n$ is a power of $2$

Published on 01 Sep 2018 - 21:59

81

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Generating prime factors of a certain congruence?

Published on 10 Oct 2018 - 10:31

197

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Are Mersenne numbers with Mersenne prime exponent always prime?

Published on 15 Oct 2018 - 10:46

104

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What are the most (and least) likely factors of a composite Mersenne number?

Published on 22 Oct 2018 - 13:04

258

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Is it possible the density of Mersenne numbers in the primes gets arbitrarily close to $1$?

Published on 26 Oct 2018 - 14:52

63

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Is any ec-number larger than $73$ the sum of a square and a cube?

Published on 05 Nov 2018 - 20:31

100

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The sum of all divisors of $N$ is a 2 potency iff $N$ is a product of different Mersenne primes

Published on 20 Nov 2018 - 14:37

140

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Do we know a $2^{M_i}-1$ that's not prime?

Published on 26 Nov 2018 - 13:15

210

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Is there an anomaly in the distribution of Mersenne primes?

Published on 22 Dec 2018 - 8:57

143

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Integers of this form that pass the Fermat Primality test are prime, proof?

Published on 13 Jan 2019 - 1:30

294

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Fibonacci primes vs Mersenne primes

Published on 25 Jan 2019 - 23:03

182

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Nested Mersenne Primes

Published on 03 Feb 2019 - 10:50

438

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Is This a New Property I Have Found Pertaining to Mersenne Primes?

Published on 27 Feb 2019 - 10:43

List Question

Disprove: If $\gcd(n,2^n-1)=1$, then $2^n-1$ is squarefree.

When $q$ is prime and a Wieferich prime $p$ divides $\ M=2^q-1\ $ . Why can we conclude $\ p^2\mid M\ $?

$b^{n}+1$ is prime only if $b\equiv0\pmod2$ and $n$ is a power of $2$

Generating prime factors of a certain congruence?

Are Mersenne numbers with Mersenne prime exponent always prime?

What are the most (and least) likely factors of a composite Mersenne number?

Is it possible the density of Mersenne numbers in the primes gets arbitrarily close to $1$?

Is any ec-number larger than $73$ the sum of a square and a cube?

The sum of all divisors of $N$ is a 2 potency iff $N$ is a product of different Mersenne primes

Do we know a $2^{M_i}-1$ that's not prime?

Is there an anomaly in the distribution of Mersenne primes?

Integers of this form that pass the Fermat Primality test are prime, proof?

Fibonacci primes vs Mersenne primes

Nested Mersenne Primes

Is This a New Property I Have Found Pertaining to Mersenne Primes?

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