Testing an integer for prime or composite character. Probabilisitc tests yield an answer with high probability of correctness, primality proofs yield an answer which is certain to be correct, often with a certificate of primality which can be verified more easily than the original proof.

Please submit sites with theoretical content, or sites that apply this theoretical content in the organized search for prime numbers. Software packages that apply these theorems should be listed under the appropriate subcategory.

Prime numbers may be considered as the building blocks of the integers, and the problems of factoring numbers into primes and discovering large primes of various forms have a definite nobility. Perhaps somewhat surprisingly, prime numbers may be proven prime without exhaustively testing all potential factors. This category includes links to theoretical information, and organized searches that apply these theorems.

Please submit sites with theoretical content, or sites that apply this theoretical content in the organized search for prime numbers. Software packages that apply these theorems should be listed under the appropriate subcategory.

Composite numbers which 'pass' probabilistic primality tests. Carmichael numbers also fall under this heading.

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