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Primes p such that p^2 divides 23^(p-1) - 1.
17

%I #15 Apr 27 2019 05:41:02

%S 13,2481757,13703077,15546404183,2549536629329

%N Primes p such that p^2 divides 23^(p-1) - 1.

%C No further terms up to 3.127*10^13.

%H Amir Akbary and Sahar Siavashi, <a href="http://math.colgate.edu/~integers/s3/s3.Abstract.html">The Largest Known Wieferich Numbers</a>, INTEGERS, 18(2018), A3. See Table 1 p. 5.

%H Richard Fischer, <a href="http://www.fermatquotient.com/FermatQuotienten/">Fermat quotients B^(P-1) == 1 (mod P^2)</a>

%t Select[Prime[Range[5*10^7]], Mod[ 23^(# - 1) - 1, #^2] == 0 &] (* _G. C. Greubel_, Jan 18 2018 *)

%t Select[Prime[Range[93*10^9]],PowerMod[23,#-1,#^2]==1&] (* _Harvey P. Dale_, May 15 2018 *)

%Y Cf. A001220, A014127, A123692, A123693, A128667, A128668, A090968, A039951

%K hard,more,nonn

%O 1,1

%A _Alexander Adamchuk_, Mar 26 2007