High Quality Content by WIKIPEDIA articles! In mathematics, a strong prime is a prime number with certain special properties. The definitions of strong primes are different in cryptography and number theory. In cryptography, a prime number p is strong if the following conditions are satisfied. 1. p is large. 2. p ? 1 has large prime factors. That is, p = a1q1 + 1 for some integer a1 and large prime q1. 3. q1 ? 1 has large prime factors. That is, q1 = a2q2 + 1 for some integer a2 and large prime q2. 4. p + 1 has large prime factors. That is, p = a3q3 ? 1 for some integer a3 and large prime q3. Sometimes a prime that satisfies a subset of the above conditions is also called strong. In some cases, some additional conditions may be included. For example, a1 = 2, or a2 = 2, etc.

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