A212287 Primes of the form m*p^2 + 1, where p is prime and m <= p^2.

5, 13, 17, 19, 37, 73, 101, 151, 197, 251, 401, 491, 601, 677, 727, 883, 1373, 1453, 1471, 1667, 2029, 2179, 2663, 3389, 3469, 3631, 3719, 4057, 4357, 4733, 5477, 6359, 6761, 7019, 8093, 8713, 8837, 9127, 9439, 9803, 9923, 10093, 10141, 10831, 10891, 11617, 11831, 12101, 12343

Offset: 1

Author

Charles R Greathouse IV, Jun 13 2012

Keywords

• nonn

Comments

Not known to be infinite, but see the Matomäki link.

Examples

			13 is a member since 13 = 3 * 2^2 + 1 with 3 <= 2^2 and 3 is prime.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
• Kaisa Matomäki, A note on primes of the form p = aq^2 + 1, Acta Arith. 137 (2009), pp. 133-137.

Crossrefs

Cf. A028916, A173587.

Programs

PARI

list(lim)=my(v=List(),t);lim=lim\1-.5;forprime(p=2,sqrt(lim), for(a=1,min(lim\p^2,p^2),if(isprime(t=a*p^2+1),listput(v,t))));vecsort(Vec(v),,8)