List questions from mersenne-numbers

Published on 23 Feb 2026 - 6:40

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Let p and q be prime numbers with $p \equiv 3 \pmod 4$ and $q=2p+1$. Prove that $2^{p} - 1$ is prime only when $p=3$

Published on 23 Feb 2026 - 6:41

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Relationship between Mersenne Primes and Triangular / Perfect Numbers

Published on 23 Feb 2026 - 6:34

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Last 3 digits of Mersenne numbers

Published on 23 Feb 2026 - 6:37

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How to check if Mersenne number is prime?

Published on 23 Feb 2026 - 6:37

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Distinct Mersenne numbers are coprime

Published on 23 Feb 2026 - 6:36

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What are some basic properties of the quotient $s_n\over M_p$ where $M_p$ is a Mersenne prime?

Published on 04 Apr 2026 - 2:10

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How can I prove that $1 + 2 + \cdots + x = \{P : P = \text{Perfect Number}\} \Leftrightarrow 2^n - 1 = x = \{M_p : n\in \mathbb{N}\}?$

Published on 23 Feb 2026 - 6:40

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Does $ \ 3\mid (M_p - 4)$?

Published on 04 Apr 2026 - 8:38

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How many numbers $2^n-k$ are prime?

Published on 23 Feb 2026 - 6:36

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Find the perfect numbers of the product of two primes, $2^p-1$ and $2^{p-1}$

Published on 23 Feb 2026 - 6:41

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lucas lehmer test.

Published on 06 Apr 2026 - 16:07

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Why are mersenne primes not wieferich primes?

Published on 23 Feb 2026 - 6:42

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How did they find the currently world's biggest known prime number?

Published on 23 Feb 2026 - 6:39

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Mersenne Primes using Mersenne Primes as n

Published on 23 Feb 2026 - 6:42

List Question

Can it be proven that the reduced digit sum of Mersenne primes, except 3 and 7, is always 1 or 4?

Let p and q be prime numbers with $p \equiv 3 \pmod 4$ and $q=2p+1$. Prove that $2^{p} - 1$ is prime only when $p=3$

Relationship between Mersenne Primes and Triangular / Perfect Numbers

Last 3 digits of Mersenne numbers

How to check if Mersenne number is prime?

Distinct Mersenne numbers are coprime

What are some basic properties of the quotient $s_n\over M_p$ where $M_p$ is a Mersenne prime?

How can I prove that $1 + 2 + \cdots + x = \{P : P = \text{Perfect Number}\} \Leftrightarrow 2^n - 1 = x = \{M_p : n\in \mathbb{N}\}?$

Does $ \ 3\mid (M_p - 4)$?

How many numbers $2^n-k$ are prime?

Find the perfect numbers of the product of two primes, $2^p-1$ and $2^{p-1}$

lucas lehmer test.

Why are mersenne primes not wieferich primes?

How did they find the currently world's biggest known prime number?

Mersenne Primes using Mersenne Primes as n

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