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For example, If my prime was congruent to 3 mod 5. Is there a list where I can find for these primes which do not take the form 3 mod 4?

Edit:

Excluding the general tonelli-shanks algorithm

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  • $\begingroup$ And what's wrong with Tonelli-Shanks? $\endgroup$ – poncho Jun 4 at 18:22
  • $\begingroup$ @poncho nothing, was wondering whether there was faster algorithms for obscure primes or a subset of them $\endgroup$ – WeCanBeFriends Jun 4 at 18:22
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    $\begingroup$ Maybe cr.yp.to/papers.html#sqroot? $\endgroup$ – Squeamish Ossifrage Jun 4 at 18:23

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