History
Mersenne primes were considered already by Euclid, who found a connection with the perfect numbers. They are named after 17th-century French scholar Marin Mersenne, who compiled what was supposed to be a list of Mersenne primes with exponents up to 257. His list was largely incorrect, as Mersenne mistakenly included M67 and M257 (which are composite), and omitted M61, M89, and M107 (which are prime). Mersenne gave little indication how he came up with his list.
Édouard Lucas proved in 1876 that M127 is indeed prime, as Mersenne claimed. This was the largest known prime number for 75 years, and the largest ever calculated by hand. M61 was determined to be prime in 1883 by Ivan Mikheevich Pervushin, though Mersenne claimed it was composite, and for this reason it is sometimes called Pervushin's number. This was the second-largest known prime number, and it remained so until 1911. Lucas had shown another error in Mersenne's list in 1876. Without finding a factor, Lucas demonstrated that M67 is actually composite. No factor was found until a famous talk by Cole in 1903. Without speaking a word, he went to a blackboard and raised 2 to the 67th power, then subtracted one. On the other side of the board, he multiplied 193,707,721 × 761,838,257,287 and got the same number, then returned to his seat (to applause) without speaking. A correct list of all Mersenne primes in this number range was completed and rigorously verified only about three centuries after Mersenne published his list.
Read more about this topic: Mersenne Prime
Famous quotes containing the word history:
“Yet poetry, though the last and finest result, is a natural fruit. As naturally as the oak bears an acorn, and the vine a gourd, man bears a poem, either spoken or done. It is the chief and most memorable success, for history is but a prose narrative of poetic deeds.”
—Henry David Thoreau (1817–1862)
“The awareness that health is dependent upon habits that we control makes us the first generation in history that to a large extent determines its own destiny.”
—Jimmy Carter (James Earl Carter, Jr.)
“In nature, all is useful, all is beautiful. It is therefore beautiful, because it is alive, moving, reproductive; it is therefore useful, because it is symmetrical and fair. Beauty will not come at the call of a legislature, nor will it repeat in England or America its history in Greece. It will come, as always, unannounced, and spring up between the feet of brave and earnest men.”
—Ralph Waldo Emerson (1803–1882)