List questions from prime-numbers

Published on 07 May 2026 - 7:50

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How to make the arithmetic progression contain infinitely many primes by adding a rational number to common difference?

Published on 10 May 2026 - 14:05

593

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The distribution of powers of primes

Published on 10 May 2026 - 12:19

198

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Does $\operatorname*{\exists}\limits^{\infty} f(n) :$ prime?

Published on 10 May 2026 - 12:37

85

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Show that $1+ \frac{1}{p} + \frac{1}{p^2} + ... + \frac{1}{p^k} = \frac{p^{k+1}-1}{p^k(p-1)}$

Published on 10 May 2026 - 12:55

37

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Primes of the form $a^{p^{n+1}} \pmod {p^n}$

Published on 11 May 2026 - 5:43

94

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Let $A(x) = \sum_{n\leq x} a(n)$, is it possible that $A(x) = π(x) + O(\sqrt x)$

Published on 03 May 2026 - 13:18

247

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On a conjecture and other numbers like $144$.

Published on 10 May 2026 - 12:37

200

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Solving $x^2+x+1=7^n$

Published on 29 Apr 2026 - 12:46

6.7k

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Prove that the nth prime number $p_n$ satisfies $p_n\leq 2^{2n-1}$

Published on 11 May 2026 - 3:13

238

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Compositeness test for repunits in base $-3$

Published on 10 May 2026 - 18:59

116

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On the conjecture that if $\,\forall\{x, y, z\}\subset \Bbb{Z^+}$ squarefree, and $\ x^3 + y^3 = z^2$, then $\gcd(3, x, y) = 1$.

Published on 10 May 2026 - 12:39

1.3k

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Stronger versions of Wilson's Theorem

Published on 16 Apr 2026 - 0:25

1.4k

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Alternating series of primes

Published on 06 Apr 2026 - 17:20

93

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What is the the nature of $(p^p \pm 1)/(p\pm 1)$?

Published on 10 May 2026 - 14:07

List Question

Landau's comment on validity of Goldbach's conjecture

How to make the arithmetic progression contain infinitely many primes by adding a rational number to common difference?

The distribution of powers of primes

Does $\operatorname*{\exists}\limits^{\infty} f(n) :$ prime?

Show that $1+ \frac{1}{p} + \frac{1}{p^2} + ... + \frac{1}{p^k} = \frac{p^{k+1}-1}{p^k(p-1)}$

Primes of the form $a^{p^{n+1}} \pmod {p^n}$

Let $A(x) = \sum_{n\leq x} a(n)$, is it possible that $A(x) = π(x) + O(\sqrt x)$

On a conjecture and other numbers like $144$.

Solving $x^2+x+1=7^n$

Prove that the nth prime number $p_n$ satisfies $p_n\leq 2^{2n-1}$

Compositeness test for repunits in base $-3$

On the conjecture that if $\,\forall\{x, y, z\}\subset \Bbb{Z^+}$ squarefree, and $\ x^3 + y^3 = z^2$, then $\gcd(3, x, y) = 1$.

Stronger versions of Wilson's Theorem

Alternating series of primes

What is the the nature of $(p^p \pm 1)/(p\pm 1)$?

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