Three New Mersenne Primes and a Statistical Theory
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چکیده
If p is prime, Mp = 2P — 1 is called a Mersenne number. If ui = 4 and «<+1 = Mj+i — 2, then M„ is prime if and only if uv-i m 0(mod Mp). This is called the Lucas test (see Lehmer [4]). The primes Mom , M mi, and Mu2W which are now the largest known primes, were discovered by Illiac II at the Digital Computer Laboratory of the University of Illinois. The computing times were 1 hour 23 minutes, 1 hour 30 minutes, and 2 hours 15 minutes respectively, and the calculations were checked by repetition. This brings to 23 the number of known Mersenne primes, namely for
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تاریخ انتشار 2010