List questions from prime-numbers

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An inequality on prime gaps

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My first proof employing strong induction / complete induction (very simple number theory). Please mark/grade.

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Proof for the existence of primes not equal to $ap_\alpha +bp_\beta$ etc?

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A function about prime numbers

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Is the product of two primes ALWAYS a semiprime?

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On the sum of prime powers

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What is the 5000th happy prime number?

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Does a solution exist where $p,q$ are odd primes and $p^a - q^b = p^c - q^d$ where $a > c > 1$ and $b > d > 1$

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Subset of prime numbers

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Connections between prime numbers and geometry

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Proving that if $a,b > 1$, then $5^a - 3^b=16$ has only one solution with $a=2$ and $b=2$

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prime powers modulo prime

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Distribution of prime numbers. Can one find all prime numbers?

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Solve for $p^a + 1 = 2\cdot q^b$ where $p,q$ are odd primes and $a,b \ge 2$

Published on 25 Mar 2026 - 17:20

List Question

Proof of convergence of $L'\left(1,\chi\right)$

An inequality on prime gaps

My first proof employing strong induction / complete induction (very simple number theory). Please mark/grade.

Proof for the existence of primes not equal to $ap_\alpha +bp_\beta$ etc?

A function about prime numbers

Is the product of two primes ALWAYS a semiprime?

On the sum of prime powers

What is the 5000th happy prime number?

Does a solution exist where $p,q$ are odd primes and $p^a - q^b = p^c - q^d$ where $a > c > 1$ and $b > d > 1$

Subset of prime numbers

Connections between prime numbers and geometry

Proving that if $a,b > 1$, then $5^a - 3^b=16$ has only one solution with $a=2$ and $b=2$

prime powers modulo prime

Distribution of prime numbers. Can one find all prime numbers?

Solve for $p^a + 1 = 2\cdot q^b$ where $p,q$ are odd primes and $a,b \ge 2$

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