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Primes p such that p^2 divides 17^(p-1) - 1.
19

%I #19 Apr 27 2019 05:40:08

%S 2,3,46021,48947,478225523351

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

%C Mossinghoff showed that there are no further terms up to 10^14.

%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>

%H M. J. Mossinghoff, <a href="http://academics.davidson.edu/math/mossinghoff/WiefPairsBarkerSeqs_MJM.pdf">Wieferich pairs and Barker sequences</a>, Des. Codes Cryptogr. 53 (2009), 149-163.

%t Select[Prime[Range[5*10^6]], Mod[ 17^(# - 1) - 1, #^2] == 0 &] (* _G. C. Greubel_, Jan 18 2018 *)

%Y Cf. A001220, A014127, A123692, A123693, A128667, A090968, A128669, A039951.

%K hard,more,nonn

%O 1,1

%A _Alexander Adamchuk_, Mar 26 2007

%E The prime 478225523351 was found by Richard Fischer on Oct 25 2005

%E Extension corrected by _Jonathan Sondow_, Jun 24 2010