View Single Post
 2021-01-23, 00:02 #16 kriesel     "TF79LL86GIMPS96gpu17" Mar 2017 US midwest 47·107 Posts Mersenne semiprimes Semiprimes are natural numbers that are products of exactly two factors other than one and themselves (and they may be squares). https://prime-numbers.info/article/semiprimes http://oeis.org/A092561 lists Mersenne numbers that are semiprimes without regard to whether n is composite. n Mn 4 15, 9 511, 11 2047, 23 8388607, 37 137438953471, 41 2199023255551, 49 562949953421311, 59 576460752303423487, 67 147573952589676412927, 83 9671406556917033397649407, 97 158456325028528675187087900671, 101 2535301200456458802993406410751 Subsetting to prime exponent < 100 gives p for Mp and factors 11 2047 f=23; 89 23 8,388,607 f=47; 178481 37 137438953471 f=223; 616318177 41 2,199,023,255,551 f=13367, 164,511,353 59 576,460,752,303,423,487 f= 179951, 3 203431 780337 67 147,573,952,589,676,412,927 = 193 707721 × 761838 257287 83 9,671,406,556,917,033,397,649,407 = 167 × 57912 614113 275649 087721 97 158,456,325,028,528,675,187,087,900,671 = 11447 × 13 842607 235828 485645 766393 below p=100, 8 Mersenne semiprimes of prime exponent vs. 10 Mersenne primes. in p= 100 to 200, 8 semiprimes vs. only 2 primes of prime exponent. in p=200 to 500, 9 vs 0. https://www.mersenne.org/report_expo..._hi=500&full=1 Last fiddled with by kriesel on 2021-01-29 at 17:22 Reason: add a semiprime definition and link