A214519
Least number m such that 4*m^2 + 1 is prime and the next prime of this form is 4*(m + A214518(n))^2 + 1.
Original entry on oeis.org
1, 3, 13, 20, 47, 92, 175, 248, 1695, 1768, 22685, 41367, 49532, 178582, 420452, 1940278, 13957468, 20258760
Offset: 1
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n = 1; last = 1; t = {1}; t2 = {1}; While[Length[t] < 10, n++; p = 1 + 4 n^2; If[PrimeQ[p], If[n - last > t[[-1]], AppendTo[t, n - last]; AppendTo[t2, last]]; last = n]]; t2
A215233
Primes of the form 4m^2 + 1 such that the next prime of this form is a record distance away.
Original entry on oeis.org
5, 37, 677, 1601, 8837, 33857, 122501, 246017, 11492101, 12503297, 2058436901, 6844914757, 9813676097, 127566122897, 707119537217, 15058714869137, 779243651884097, 1641669426950401, 10965274367622437, 1269017804759665217, 4346851918104880901
Offset: 1
See
A215234 for the next larger prime of the form 4m^2 + 1.
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r=0;last=2;forstep(n=4,1e9,2, if(!ispseudoprime(n^2+1),next); if(n-last>r, r=n-last; print1(last^2+1", ")); last=n) \\ Charles R Greathouse IV, Apr 09 2013
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