List questions from prime-factorization

Published on 20 Sep 2023 - 6:30

108

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Open Question: For natural $n$ with prime decomposition $\prod p_i^{r_i}$, define $f(n)=\sum p_i r_i$. Find all $n$ such that $f(n)-f(n+1)=1$.

Published on 22 Sep 2023 - 22:59

67

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All possible factorisations of a number

Published on 23 Sep 2023 - 11:21

55

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ways to write out a number in exponential form

Published on 24 Sep 2023 - 4:53

30

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Form of the divisors of a number (Prime Factorization). Is this algorithm-based proof correct?

Published on 28 Sep 2023 - 13:42

460

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Is this algorithm efficient as a factorization algorithm?

Published on 29 Sep 2023 - 12:34

79

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Is the quadratic sieve algorithm on Wikipedia wrong/inefficient?

Published on 25 Mar 2026 - 16:13

57

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Why trial division algorithm to find the prime factors of $N$ is $O(\sqrt{N})$, even though you need to check after $\sqrt{N}$?

Published on 06 Oct 2023 - 11:55

81

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Composite Prime Test to determine distance between P and Q

Published on 12 Oct 2023 - 5:29

301

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Center Binomial can "Self-Factor" RSA semiprimes.

Published on 13 Oct 2023 - 2:13

54

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Ramification of primes on $\overline{\mathbb Q}$

Published on 25 Mar 2026 - 9:53

92

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Is $\omega(n)=16$ the maximum?

Published on 30 Mar 2026 - 10:09

79

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Dottie number and prime factorization

Published on 28 Mar 2026 - 17:05

51

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Found a relation regarding the primes, is this interesting?

Published on 29 Mar 2026 - 3:44

249

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Prime factors of $5^n+6^n+7^n+8^n+9^n+10^n$

Published on 15 Nov 2023 - 18:18

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Show for some n Fermat’s method is faster than reverse trial division

Open Question: For natural $n$ with prime decomposition $\prod p_i^{r_i}$, define $f(n)=\sum p_i r_i$. Find all $n$ such that $f(n)-f(n+1)=1$.

All possible factorisations of a number

ways to write out a number in exponential form

Form of the divisors of a number (Prime Factorization). Is this algorithm-based proof correct?

Is this algorithm efficient as a factorization algorithm?

Is the quadratic sieve algorithm on Wikipedia wrong/inefficient?

Why trial division algorithm to find the prime factors of $N$ is $O(\sqrt{N})$, even though you need to check after $\sqrt{N}$?

Composite Prime Test to determine distance between P and Q

Center Binomial can "Self-Factor" RSA semiprimes.

Ramification of primes on $\overline{\mathbb Q}$

Is $\omega(n)=16$ the maximum?

Dottie number and prime factorization

Found a relation regarding the primes, is this interesting?

Prime factors of $5^n+6^n+7^n+8^n+9^n+10^n$

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