A145741 Numbers p such that p + 4*m^2 is prime for m = 0,1,2,3,...,10.

163, 409333, 1867783, 828497443, 2059599067, 5767711867, 8965599883, 9655686727, 9671300983, 12627473917, 19635778453, 31428255373, 76292280733, 140192390683, 141077258953, 141805795657, 150360096973, 176552953273, 186521536807, 250298387047

Offset: 1

Author

Farideh Firoozbakht, Oct 17 2008

Keywords

• nonn

Comments

It is obvious that all terms are prime.

A very strange and interesting thing related to the first term: All 20 numbers 163+4*m^2 for m=0,1,2,...,19 are prime.

There are 3136 terms below 10^15, ending with 999926956948957. - Jens Kruse Andersen, Oct 24 2008

Examples

			All 11 numbers 2059599067 + 4*m^2 for m = 0,1,2,...,10 are prime, so 2059599067 is a term.
		

Links

• Jens Kruse Andersen, Table of n, a(n) for n = 1..3136
• Carlos Rivera, Consecutive even squares+prime=prime.
• Carlos Rivera, Puzzle 464. p+4*x^2.

Crossrefs

Cf. A145742, A145743.

Programs

PARI

forprime(p=1,5*10^8,c=0;for(m=1,10,if(!isprime(p+4*m^2),break);c+=1);if(c==10,print1(p,", "))) \\ Derek Orr, Jul 25 2017

Extensions

More terms from Jens Kruse Andersen, Oct 24 2008