Wieferich primes

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Tomasz Ordowski

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Aug 21, 2026, 8:51:03 AM (6 days ago) Aug 21
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Hello again! 

Conjecture: if 2^(p-1) == 1 (mod p^2),
then phi(p^2)+1 = (p-1)p+1 = q prime. 
If so, then 2^(q-1) == 1 (mod p^3).
For p = 1093 and 3511 it works! 
Is this a double coincidence?! 
If not, narrowing the search 
to such cases could yield 
a third Wieferich prime.

Best, 

Tom Ordo 
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