1006003

Properties

Appears in sequences

• Mirimanoff primes: primes p such that p^2 divides 3^(p-1) - 1.at n=1A014127
• Least prime p such that (p,q) is a Double Wieferich prime pair for q=A124121(n).at n=1A124122
• GCDs arising in A126196.at n=7A126197
• Smallest prime p such that there exist exactly n integers b such that 1 < b < p and b^(p-1) == 1 (mod p^2) or, equivalently, Fermat quotient q_p(b) == 0 (mod p).at n=12A175932
• 2nd Wieferich prime base prime(n).at n=1A178871
• Numbers n such that 3^phi(n) == 1 (mod n^2), where phi(n) is Euler's totient function.at n=8A242958
• Primes p that set a new record for the number of bases 1 < b < p for which p is a base-b Wieferich prime.at n=7A248865
• Primes q with A253683(n) > q > A253685(n) such that (A253683(n), q, A253685(n)) forms a Wieferich triple.at n=10A253684
• n-th Wieferich prime to base prime(n), i.e., primes p such that p is the n-th solution of the congruence (prime(n))^(p-1) == 1 (mod p^2).at n=1A259909
• Primes p such that A001221(p-1)^(p-1) == 1 (mod p^2).at n=7A260377
• Primes p such that a prime q < p exists with p^(q-1) == 1 (mod q^2) and q^(p-1) == 1 (mod p^2), i.e., primes that are the larger member of a double Wieferich prime pair.at n=4A266829
• Second base-n Wieferich prime, i.e., second smallest prime p such that n^(p-1) == 1 (mod p^2).at n=1A268352
• Square array read by antidiagonals downwards: A(n, 1) = second Wieferich prime to base n and A(n, k) = second Wieferich prime to base A(n, k-1) for k > 1.at n=2A281002
• Two-column array A(n, k) read by rows, where A(n, 1) and A(n, 2) respectively give values of q and p in the n-th double Wieferich prime pair, where p > q. Terms sorted first by increasing size of p, then by increasing size of q.at n=9A282293
• Primes p such that Omega(p + 1)^(p - 1) == 1 (mod p^2), where Omega is A001222.at n=6A306909
• Primes p that satisfy q^(p-1) == 1 (mod p^2), i.e., are base-q Wieferich primes, for a prime q dividing p-1.at n=3A355545
• Prime numbersat n=78940