Question

Does this explicit formula for the prime-counting function $\pi(x)$ converge?

score 214 · Answer 1 · 2019-04-21 19:33:33

214

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Does this explicit formula for the prime-counting function $\pi(x)$ converge?

Published on 21 Apr 2019 - 19:33

score 81 · Answer 2 · 2026-03-29 05:44:17

81

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Given $p_1^{a_1}+ \dots + p_r^{a_r} \leq n$, show that : $r \leq 2\sqrt{\frac{n}{\log(n)}}(1+o(1))$

Published on 29 Mar 2026 - 5:44

score 97 · Answer 3 · 2026-03-25 17:21:48

97

Views

Are there infinitely many solutions such that the digit sum of a prime power is a smaller power of the same prime?

Published on 25 Mar 2026 - 17:21

score 492 · Answer 4 · 2026-03-23 09:53:29

492

Views

Primality test for numbers of the form $N=k \cdot 3^n-1$

Published on 23 Mar 2026 - 9:53

score 1.5k · Answer 5 · 2019-04-22 12:45:12

1.5k

Views

Distribution of prime numbers modulo $4$

Published on 22 Apr 2019 - 12:45

score 104 · Answer 6 · 2026-03-25 04:43:57

104

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Are 2, 3 the only prime numbers that don't have the digit 1 and are palindromes whose squares are also palindromes?

Published on 25 Mar 2026 - 4:43

score 1.4k · Answer 7 · 2026-03-26 19:35:48

1.4k

Views

Computing Integers' Prime Factorization Using the General Number Field Sieve

Published on 26 Mar 2026 - 19:35

score 95 · Answer 8 · 2019-04-23 03:31:00

95

Views

Find all primes $p$ for which $19 p - 1$ is a perfect cube

Published on 23 Apr 2019 - 3:31

score 167 · Answer 9 · 2026-03-28 05:23:28

167

Views

Find the smallest $n$ such that the $n$-th prime $p_n \equiv 330 \mod n $.

Published on 28 Mar 2026 - 5:23

score 135 · Answer 10 · 2026-03-25 14:20:16

135

Views

Reasoning about remainders and the Möbius function

Published on 25 Mar 2026 - 14:20

score 275 · Answer 11 · 2026-03-25 04:42:55

275

Views

Pairs of palindromic primes without $1$ and have a palindromic product

Published on 25 Mar 2026 - 4:42

score 111 · Answer 12 · 2026-03-26 06:05:27

111

Views

Should you use Euler's generalization of fermat's little theorem for primality testing?

Published on 26 Mar 2026 - 6:05

score 269 · Answer 13 · 2026-03-26 18:40:53

269

Views

How to find the number of trailing zeros in a factorial?

Published on 26 Mar 2026 - 18:40

score 74 · Answer 14 · 2026-03-28 10:19:10

74

Views

How many primes and semiprimes are generated by this sum?

Published on 28 Mar 2026 - 10:19

score 70 · Answer 15 · 2026-03-25 06:12:04

70

Views

Showing that for $x \ge 7$, $x\# \ge x^2+x$

Published on 25 Mar 2026 - 6:12

List Question

Does this explicit formula for the prime-counting function $\pi(x)$ converge?

Given $p_1^{a_1}+ \dots + p_r^{a_r} \leq n$, show that : $r \leq 2\sqrt{\frac{n}{\log(n)}}(1+o(1))$

Are there infinitely many solutions such that the digit sum of a prime power is a smaller power of the same prime?

Primality test for numbers of the form $N=k \cdot 3^n-1$

Distribution of prime numbers modulo $4$

Are 2, 3 the only prime numbers that don't have the digit 1 and are palindromes whose squares are also palindromes?

Computing Integers' Prime Factorization Using the General Number Field Sieve

Find all primes $p$ for which $19 p - 1$ is a perfect cube

Find the smallest $n$ such that the $n$-th prime $p_n \equiv 330 \mod n $.

Reasoning about remainders and the Möbius function

Pairs of palindromic primes without $1$ and have a palindromic product

Should you use Euler's generalization of fermat's little theorem for primality testing?

How to find the number of trailing zeros in a factorial?

How many primes and semiprimes are generated by this sum?

Showing that for $x \ge 7$, $x\# \ge x^2+x$

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