# [seqfan] Re: Prime Diophantine p = 2*q^2 + r.

Richard Guy rkg at cpsc.ucalgary.ca
Sun Nov 23 18:05:22 CET 2008

```2*(6n +/- 1)^2 + (6m+1) = 3*(24n^2 +/- 8n + 2m +1)  R.

On Sun, 23 Nov 2008, zak seidov wrote:

> Consider Prime Diophantine p=2q^2+r with p, q, r all primes.
>
> Apparently there aren't solutions for r=
> 2, 7, 31, 37, 67, 73, 97, 103, 127, 151, 157, 199, 229, 241, 271, 277, 283, 307, 337, 367, 373, 397, 409, 433, 457, 463, 487, 499, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997.
>
> Case r=2 is trivial (even for me :)) but what about other cases?
>
> Anyone may wish to check/confirm/reject the list,
> thx, zak
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