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Number theory
Hardy Littlewood - first hardy littlewood conjecture
Let P=(m1,…,mk) be a tuple of distinct positive even integers. Let
πP(n)
denote the number of primes
p≤n
such that
(p,p+m1,…,p+mk)
forms an admissible prime constellation. Let
w(q;m1,…,mk)
denote the
number of distinct residues of
0,m1,…,mk
modulo
q
, and let
CP=2kqprimeq≥3∏(1−q1)k+11−qw(q;m1,…,mk).
Then
πP(n)∼CP∫2nlogk+1tdt.
$2,735 bounty·nobody has started
week of 29 Sept 2025 · nothing publishedweek of 6 Oct 2025 · nothing publishedweek of 13 Oct 2025 · nothing publishedweek of 20 Oct 2025 · nothing publishedweek of 27 Oct 2025 · nothing publishedweek of 3 Nov 2025 · nothing published
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29 Sept 2025nothing published against this one yet21 Sept 2026
Wikipedia
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