Most people chasing new Mersenne primes — the rare numbers of the form 2^p - 1 — look for the real thing: big, beautiful primes used in encryption and number theory.
But while studying these, we found something odd:
Some composite numbers built from the same formula look exactly like Mersenne primes in binary — 100% 1’s, no difference in structure — and only fail at deeper primality tests.
We believe:
• These “Mersenne impostors” could help sharpen how we screen for real primes
• They might even explain false-positive cases in cryptographic applications
• And this pattern doesn’t seem to be documented in any major research database
But while studying these, we found something odd:
Some composite numbers built from the same formula look exactly like Mersenne primes in binary — 100% 1’s, no difference in structure — and only fail at deeper primality tests.
We believe: • These “Mersenne impostors” could help sharpen how we screen for real primes • They might even explain false-positive cases in cryptographic applications • And this pattern doesn’t seem to be documented in any major research database