A145743 -id:A145743 - 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

A145742 Composite numbers n such that all 10 numbers n+4*m^2 for m=1,2,...,10 are prime.

Original entry on oeis.org

143473, 2821813, 3171877, 27439003, 95771533, 107832187, 174499873, 315915517, 438561313, 761271373, 1010315923, 1083101167, 1247119687, 1272171217, 1494582637, 1540272427, 2760699643, 3205014607, 3615583147, 3636010807

Offset: 1

Farideh Firoozbakht, Oct 17 2008

nonn

There is no further term up to 2*10^8.

			174499873 is composite and all 10 numbers 174499873+4m^2 for m=1,2,...,10 are prime.

Cf. A145741, A145743.

Select[Range[140001,364*10^7,2],CompositeQ[#]&&AllTrue[#+{4,16,36,64,100,144,196,256,324,400},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jun 12 2017 *)

a(8)-a(20) 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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