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 A306501 Primes p such that 2, 3, 5, 7, ..., 37 are all quadratic nonresidues modulo p. 1
 163, 74093, 92333, 170957, 222643, 225077, 253507, 268637, 292157, 328037, 360293, 517613, 524453, 530837, 613637, 641093, 679733, 781997, 847997, 852893, 979373, 991027, 1096493, 1110413, 1333963, 1398053, 1730357, 1821893, 2004917, 2055307, 2056147, 2079173 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The prime number 163 is famous for having 2, 3, 5, 7, ..., 37 as quadratic nonresidues, because the smallest prime having 2, 3, 5, 7, ..., 41 as quadratic nonresidues, namely 74093, is 453.5 times larger. This is related to the fact that the quadratic field Q[sqrt(-163)] is a unique factorization domain. If p is in the sequence then so are all primes q with q == p (mod 29682952539240), where 29682952539240 = 2^3*3*5*7*11*13*17*19*23*29*31*37. In particular, the sequence is infinite. - Robert Israel, Mar 31 2019 LINKS Robert Israel, Table of n, a(n) for n = 1..2694 MAPLE N:= 3*10^6: # to get all terms <= N S:= {seq(8*i+3, i=1..(N-3)/8)} union {seq(8*i+5, i=1..(N-5)/8)}: for p in select(isprime, [\$3..37]) do   R:= select(t -> numtheory:-legendre(t, p) = 1, {\$1..p-1});   if p mod 4 = 1 then S:= remove(t -> member(t mod p, R), S)   else S:= select(t -> member(t mod p, R) = evalb(t mod 4 = 3), S)   fi; od: sort(convert(select(isprime, S), list)); # Robert Israel, Mar 31 2019 PROG (PARI) forprime(p=2, 1e6, if(sum(k=1, 37, isprime(k)*kronecker(k, p))==-12, print1(p, ", "))) CROSSREFS Cf. A191089. Sequence in context: A217963 A138200 A146504 * A247269 A145741 A247273 Adjacent sequences:  A306498 A306499 A306500 * A306502 A306503 A306504 KEYWORD nonn AUTHOR Jianing Song, Feb 19 2019 STATUS approved

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Last modified February 26 21:58 EST 2020. Contains 332295 sequences. (Running on oeis4.)