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Results tagged with prime-numbers
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user 2480
Questions where prime numbers play a key-role, such as: questions on the distribution of prime numbers (twin primes, gaps between primes, Hardy–Littlewood conjectures, etc); questions on prime numbers with special properties (Wieferich prime, Wolstenholme prime, etc.). This tag is often used as a specialized tag in combination with the top-level tag nt.number-theory and (if applicable) analytic-number-theory.
6
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0
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Can integers be distorted to make primes more regular?
Given a set $P$ of real numbers $\ge 1$, define the gap among different products in $P$ as
$$g(P) = \inf \big\{\prod_{i=1}^n p_i^{a_i} - \prod_{i=1}^n p_i^{b_i} \mid p_i\in P;\,\, p_i\ne p_j \,\text{ …
- 5,103
9
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Prime square offsets: Why is +7 more frequent than -7?
Modulo 6 the squares are 0,1,4,3,4,1 and the squares+7 (or -5) can only be 1,2,5,4,5,2, of which 3/6 can at all be prime. The squares-7 (or +5) are 5,0,3,2,3,0 of which only 1/6 can be prime. Obviousl …
- 5,103
1
vote
Sum of two squares and implication of Bunyakovsky conjecture
Notice that in your example
$(a1-\textit{i}*a2)*(-4+3\textit{i})/5 = a3-\textit{i}*a4$.
$\mathbb{Z}[\textit{i}]$ is UFD and so is $\mathbb{Z}[\textit{i}][x]$.
- 5,103