Questions tagged [semiprimes]

A semiprime is a natural number that is the product of two prime numbers. This tag is intended for questions about, related to, or involving semiprime numbers.

A semiprime, also called a 2-almost prime, biprime or pq-number, is a composite number that is the product of two (possibly equal) primes. The first few are 4, 6, 9, 10, 14, 15, 21, 22, ... (OEIS A001358).

Semiprimes are highly useful in the area of cryptography and number theory, most notably in public key cryptography, where they are used by RSA. It relies on the fact that finding two large primes and multiplying them together (resulting in a semiprime) is computationally simple, whereas finding the original factors appears to be difficult.

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Chen’s Theorem with conditional semiprimes

Chen’s Theorem states that every sufficiently large even integer can be written as the sum of a prime and a prime or a semiprime (the product of two, not necessarily distinct, primes). Let’s consider the case ‘prime + semiprime’. $$N = p + P2$$ I’m…
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Is it possible to generate a 1000 digit semiprime without knowing its two primes?

I studied this question. I'd like to modify it to make it more interesting and more challenging. Is it possible to generate a (very large, say, with 1000 digits) semiprime without knowing its two primes? If not, is it possible to do so with a high…