|
%I #13 Feb 18 2023 10:39:21
%S 163,409333,1867783,828497443,2059599067,5767711867,8965599883,
%T 9655686727,9671300983,12627473917,19635778453,31428255373,
%U 76292280733,140192390683,141077258953,141805795657,150360096973,176552953273,186521536807,250298387047
%N Numbers p such that p + 4*m^2 is prime for m = 0,1,2,3,...,10.
%C It is obvious that all terms are prime.
%C 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.
%C There are 3136 terms below 10^15, ending with 999926956948957. - _Jens Kruse Andersen_, Oct 24 2008
%H Jens Kruse Andersen, <a href="/A145741/b145741.txt">Table of n, a(n) for n = 1..3136</a>
%H Carlos Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_461.htm">Consecutive even squares+prime=prime</a>.
%H Carlos Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_461.htm">Puzzle 464. p+4*x^2</a>.
%e All 11 numbers 2059599067 + 4*m^2 for m = 0,1,2,...,10 are prime, so 2059599067 is a term.
%o (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
%Y Cf. A145742, A145743.
%K nonn
%O 1,1
%A _Farideh Firoozbakht_, Oct 17 2008
%E More terms from _Jens Kruse Andersen_, Oct 24 2008
|
