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A079544
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Primes of the form x^2 + y^2 + 1, x>0, y>0.
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4
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3, 11, 19, 41, 53, 59, 73, 83, 101, 107, 131, 137, 149, 163, 179, 181, 227, 233, 251, 293, 307, 347, 389, 401, 443, 467, 491, 521, 523, 563, 587, 593, 613, 641, 677, 739, 773, 809, 811, 821, 883
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OFFSET
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1,1
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COMMENTS
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Sequence is known to be infinite due to a result of Linnik.
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REFERENCES
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D. S. Mitrinovic et al., Handbook of Number Theory, Kluwer, p. 11.
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LINKS
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MATHEMATICA
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iMax=7!; a=Floor[Sqrt[iMax]]; lst={}; Do[Do[p=x^2+y^2+1; If[PrimeQ@p&&p<=iMax, AppendTo[lst, p]], {y, 1, a}], {x, 1, a}]; Union[lst] (* Vladimir Joseph Stephan Orlovsky, Aug 11 2009 *)
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PROG
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(PARI) list(lim)=my(v=List(), t); lim\=1; for(x=1, sqrtint(lim-2), forstep(y=2-x%2, min(x, sqrtint(lim-x^2-1)), 2, if(isprime(t=x^2+y^2+1), listput(v, t)))); vecsort(Vec(v), , 8) \\ Charles R Greathouse IV, Jun 13 2012
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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