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A275878 Standard Jacobi primes.

%I A275878 #24 Jul 29 2022 03:37:45
%S A275878 7,61,331,547,1951,2437,3571,4219,7351,8269,9241,10267,13669,23497,
%T A275878 25117,55897,60919,74419,89269,92401,102121,112327,115837,126691,
%U A275878 145861,170647,202021,231019,241117,246247,251431,267307,283669,329677,347821,360187,372769
%N A275878 Standard Jacobi primes.
%C A275878 From _Peter Bala_, Feb 20 2022: (Start)
%C A275878 Primes of the form (3*k + 2)^3 - (3*k + 1)^3 = 27*k^2 + 27*k + 7.
%C A275878 Equivalently, primes p such that 4*p = 27*x^2 + 1, where x is odd.
%C A275878 Primes p of the form 6*m + 1, where 8*m + 1 is an odd square.
%C A275878 A prime p is in this list iff binomial(2*(p-1)/3,(p-1)/3) == -1 (mod p). See Cosgrave and Dilcher, Theorem 5, Corollary 3. (End)
%C A275878 Subsequence of cuban primes (A002407). - _Bernard Schott_, Jul 28 2022
%H A275878 Dana Jacobsen, <a href="/A275878/b275878.txt">Table of n, a(n) for n = 1..10000</a>
%H A275878 John B. Cosgrave and Karl Dilcher, <a href="https://doi.org/10.4169/amer.math.monthly.118.09.812">An Introduction to Gauss Factorials</a>, Amer. Math. Monthly, Vol. 118, No. 9 (November 2011), pp. 812-829.
%H A275878 J. B. Cosgrave and Karl Dilcher, <a href="https://www.johnbcosgrave.com/perch/resources/07-a-role-...-with-dedication.pdf">A role for generalized Fermat numbers</a>, Math. Comp., to appear 2016; see also <a href="http://johnbcosgrave.com/publications.php">Paper #10</a>, See Table 7.1.
%o A275878 (Perl) use ntheory ":all"; forprimes { if (($_%3)==1) { my $z = znorder(factorial(($_-1)/3),$_); $z/=3 unless $z%3; say if $z==1; } } 1e6; # _Dana Jacobsen_, Aug 18 2016
%o A275878 (Perl) use ntheory ":all"; for (0..1000) { my $p = 27*$_*$_ + 27*$_ + 7; say $p if is_prime($p); } # _Dana Jacobsen_, Aug 18 2016
%Y A275878 Cf. A002407, A275879.
%K A275878 nonn
%O A275878 1,1
%A A275878 _N. J. A. Sloane_, Aug 17 2016
%E A275878 Terms a(21) and beyond from _Dana Jacobsen_, Aug 18 2016