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

1,1

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

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.

Example

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

Prog

(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

Crossrefs

Cf. A145742, A145743.

Sequence in context: A146504 A306501 A247269 * A247273 A247275 A247276

Adjacent sequences: A145738 A145739 A145740 * A145742 A145743 A145744

Keyword

nonn

Author

Farideh Firoozbakht, Oct 17 2008

Extensions

More terms from Jens Kruse Andersen, Oct 24 2008

Status

approved