Hello, sometime ago, someone came up with 26 primes in arith. progression. The calculation was hard and took 6 months of intense CPU time. https://en.wikipedia.org/wiki/Primes_in_arithmetic_progression But what if the primes are in geometric progression instead like a(n) = { c^n } , where { } is the nearest integer. For example if c = 2.553854696... then the primes are : 3, 7, 17, 43, 109, 277, 709. Only 7 of them. Can we find better ? By using a Monte-Carlo + Simulated Annealing method, one can find much more. Here is a small table : Value of c : range : number of primes generated 2027.167168476491219434395... n = 1..97 : 97 primes 31622.7767185595693… n = 2..388 : 387 primes (see A332308) 55237.07504296764715433124 n = 2 ..633 : 632 primes (see A333127) A conjecture is then : if c is large enough, arbitrary long chain of primes can be generated. The data about this is here : http://plouffe.fr/NEW/ I could not find any mention of <primes in geometric progression> in literrature. Best regards, Simon Plouffe