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Old 2020-06-15, 10:24   #1
Mar 2018

20F16 Posts
Smile 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 2020-06-16 at 09:57
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