A145742 -id:A145742 - cp's OEIS frontend

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

Farideh Firoozbakht, Oct 17 2008

nonn

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

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

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.

Cf. A145742, A145743.

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

More terms from Jens Kruse Andersen, Oct 24 2008

A145743 a(n) is the smallest composite number m such that all n numbers m+4*k^2 for k=1,2,...,n are prime.

Original entry on oeis.org

9, 15, 25, 25, 247, 583, 5377, 143473, 143473, 143473, 2821813, 62087033647, 91450844347

Offset: 1

Farideh Firoozbakht, Oct 17 2008

There is no further term up to 5*10^8.

Cf. A145741, A145742.

a(12)-a(13) from Donovan Johnson, Nov 17 2008

cp's OEIS Frontend

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

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