Is there any work done on prime numbers which are equidistant means like (11,17,23,29)..?what is the maximum length of such group means the group of primes which are equidistant...like the group I have mentioned is of length 4.
2026-02-23 10:20:07.1771842007
What's the maximum length of a sequence of equidistant primes?
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By the Green-Tao theorem, there are arbitrarily long arithmetic progressions consisting of prime numbers.
The first known case of 26 primes in an arithmetic progression (found in 2010) is
$$ 43\,142\,746\,595\,714\,191 + 5\,283\,234\,035\,979\,900 \cdot n, \quad\mbox{ for } n = 0 \ldots25. $$