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How would I be able to check if a given number is a solinas prime?

Using sage, how would I be able to check whether a given number is a general mersenne prime, or if possible any other special primes?

In particular, looking to check for special primes p such that modulo p is easy to calculate

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How would I be able to check if a given number is a solinas prime?

Using sage, how would I be able to check whether a given number is a general mersenne prime, or if possible any other special primes?

In particular, looking to check for special primes p such that modulo p is easy to calculate