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Building on the same context of this question

Is it possible to enforce constraints on the properties of the generated prime? For example, I'm trying to find a prime $p$ in the range specified in the question on top with the property that $5 \in QR_p$ which mean that there exists a number $x$ such that $x^2 \equiv 5\pmod p$

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2
  • $\begingroup$ I'd generate a number of primes, and then test each. $\endgroup$
    – David G. Stork
    Jan 24 '18 at 20:03
  • $\begingroup$ could you at least put your criteria in mathematica form? $\endgroup$
    – george2079
    Jan 24 '18 at 20:30
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How about

randprime[] := RandomPrime[{BitShiftLeft[2^^1001110011, 190], 
  BitShiftLeft[2^^1001110011 + 1, 190] - 1}]

NestWhile[randprime[] &, 0, JacobiSymbol[5, #] != 1 &]

984243528019146533777127966928980517167883028753863934494399
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