Marin Mersenne (1588–1648) was a French friar who became the beating heart of European science — long before scientific journals existed, he was the journal. From his monastery cell in Paris he wrote letters to everyone who mattered — Descartes, Fermat, Galileo, Pascal — passing ideas back and forth so that discoveries could spread. He was basically a one-man internet in a monk's robe.
Mersenne loved primes of a special shape,
In 1644 Mersenne boldly published a list of which exponents he thought gave primes — and got several entries wrong! He missed some and wrongly included others, and it took mathematicians nearly 300 years to fully check his claims (the errors were only settled in the 20th century). But the audacity of the guess is exactly what made it useful: a bold, checkable conjecture is worth more than cautious silence. His real genius, though, was connection — he threw the parties, so to speak, where the great minds of the age argued and grew.