currently R36 (with CK=33791) at n=10K, with these k's remain: {1148, 1555, 2110, 2133, 3699, 4551, 4737, 6236, 6883, 7253, 7362, 7399, 7991, 8250, 8361, 8363, 8472, 9491, 9582, 11014, 12320, 12653, 13641, 14358, 14540, 14836, 14973, 14974, 15228, 15687, 15756, 15909, 16168, 17354, 17502, 17946, 18203, 19035, 19646, 20092, 20186, 20630, 21880, 22164, 22312, 23213, 23901, 23906, 24236, 24382, 24645, 24731, 24887, 25011, 25159, 25161, 25204, 25679, 25788, 26160, 26355, 27161, 29453, 29847, 30970, 31005, 31634, 32302, 33047, 33627}, I know that square k's proven composite by full algebra factors (except k=1, since for n=2, (1*36^2-1)/gcd(1-1,36-1) = 37 is prime, however k=1 can only have this prime and cannot have no more primes (thus cannot have infinitely many primes), thus k=1 is still excluded from the conjecture (see post

https://mersenneforum.org/showpost.p...&postcount=315 for more information), a k-value is included from the conjecture if and only if this k-value

*may* have infinitely many primes; also, I know that the k's such that gcd(k-1,36-1) = 1 is completely the same as the R36 problem in CRUS for these k's, however I don't have the primes for these k's other than the top 10 primes in CRUS (since gcd(33791-1,36-1) is not 1, thus the CK for the CRUS R36 conjecture cannot be 33791 (it is 116364)), thus I only listed the (probable) primes for n<=10K (in which I have searched) in the file, the (probable) primes for 1K<n<=10K are in post

https://mersenneforum.org/showpost.p...&postcount=779