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Let $k\geq 3$. Are there $k$ consecutive primes in arithmetic progression?
#141
:
[Er97c]
additive combinatorics
,
primes
,
arithmetic progressions
Green and Tao
[GrTa08]
have proved that there must always exist some $k$ primes in arithmetic progression, but these need not be consecutive. Erdős called this conjecture 'completely hopeless at present'.
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