Pg(75894) and pg(56238) and other random pg(x)
Pg(75894) and pg(56238) are primes or at least probable primes
I noticed that 75894 and 56248 are multiple of 546 and congruent to 24 mod 54
Using Wolphram (Chinese remainder theorem) I was looking for x congruent to 0 mod 546 and x congruent to 24 mod 54.
the solution is 2184+...
I noticed that 56238=(10^3+1)*54+2184 and 75894=(10^3+1)*54+2184*10
75894 and 56238 have the same residue 1638 mod 2184
There are two primes pg(19179) and pg(39699)
19179 and 39699 are congruent to 43*3^k mod 1638, for some k
19179 and 39699 are the only exponents found leading to a prime that are of the form 9*q where q is odd
19179=2131*9 and curiously also
pg(2131) is prime
Curious that 75894 and 56238 multiple of 546 are congruent to 546 mod 1092 where 1092 is a wieferich prime minus one.
Last fiddled with by enzocreti on 20200616 at 09:57
