List questions from mersenne-numbers

Published on 09 Apr 2026 - 3:15

87

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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 Feb 2026 - 23:11

191

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

Published on 22 Feb 2026 - 23:12

95

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Generating prime factors of a certain congruence?

Published on 06 Apr 2026 - 7:42

198

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Are Mersenne numbers with Mersenne prime exponent always prime?

Published on 22 Feb 2026 - 23:08

105

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

Published on 22 Feb 2026 - 23:11

259

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

Published on 22 Feb 2026 - 23:11

64

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

Published on 22 Feb 2026 - 23:10

101

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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 22 Feb 2026 - 23:12

141

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

Published on 22 Feb 2026 - 23:08

211

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Is there an anomaly in the distribution of Mersenne primes?

Published on 22 Feb 2026 - 23:10

144

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

Published on 22 Feb 2026 - 23:10

296

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Fibonacci primes vs Mersenne primes

Published on 22 Mar 2026 - 11:17

185

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Nested Mersenne Primes

Published on 05 Apr 2026 - 16:54

439

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

Published on 22 Feb 2026 - 23:10

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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