Hello, Yes, there is : a formula of Mills (1951) and Wright , but last year I have found better than those 2 formulas here : https://arxiv.org/ftp/arxiv/papers/1901/1901.01849.pdf and a more recent version here : https://vixra.org/pdf/1902.0036v1.pdf but in french. http://plouffe.fr/NEW/Un%20record%20pour%20les%20nombres%20premiers.pdf and here : http://plouffe.fr/Record%20100%20primes%20sequence.txt Actually these formulas are growing very fast even when the double exponential has a value of 1.01 So I calculated several examples of sequences of primes that are growing less rapidly : http://plouffe.fr/NEW/ you will see 2 examples. Now the conjecture is : if c is large enough then the chain of primes will be larger and larger. The record so far is 633 primes in a row. Simon Plouffe Le mer. 3 juin 2020 à 17:06, Gareth McCaughan <gareth.mccaughan@pobox.com> a écrit :
On 01/06/2020 15:55, Simon Plouffe wrote:
sometime ago, someone came up with 26 primes in arith. progression. ... But what if the primes are in geometric progression instead like a(n) = { c^n } , where { } is the nearest integer.
Isn't there a famous theorem saying that with some form like { c^c^n } or {3^3^cn} or something of the kind you can get _only_ primes?
-- g
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun