2008-11-28, 11:02 | #1 |
Mar 2006
Germany
43·67 Posts |
Special n
Here is the place to post your search-results for special exponents.
It's like a Constant n Search but i think it's worth an own thread. For example: L.Zhou searches for General Mersenne Primes, a prime with an exponent like k=1. So 755061*2^756839-1 is a General Mersenne Prime for M32 (= 2^756839-1). Next: He also searches for n=2^2^19 = 524288 so 428079*2^524288-1 is the first prime. Another: The next exponent is the 29th Fibonacci-Number (f(n)=f(n-1)+f(n-2) with f(0)=0, f(1)=1) and he found 3681*2^514229-1 as first prime! Only some examples so you can imagine when posting here. I'll expand the examples with some results when ready. |
2009-02-19, 04:28 | #2 |
Apr 2004
3×61 Posts |
n = 2^x-1 (one less than power of two)
Here are some old searches (2002) where n is one less than a power of 2
k*2^(2^15-1)-1 to 60k [56083] k*2^(2^16-1)-1 to 300k [130141, 133471, 202881, 205851, 247765, 280731, 281383, 287769, 291771] k*2^(2^17-1)-1 to 10000000 [49905, 105915, 108141, 162589, 290173, 323721, 335323, 336289, 402033, 402933, 406875, 449259, 756901, 873495, 939603, 1042009, 1164781, 1167529, 1426411, 1444729, 1519773, 1541373, 1550395, 1747023, 1829443, 1881643, 1905385, 2086119, 2114689, 2153089, 2185195, 2204653, 2317309, 2408185, 2413405, 2433045, 2462175, 2552121, 2558013, 2588301, 2637565, 2646601, 2708103, 2744811, 2825209, 2893609, 2974281, 3004861, 3028293, 3081639, 3104061, 3159709, 3347109, 3390919, 3493303, 3609655, 4063821, 4077655, 4164993, 4183761, 4193803, 4385313, 4541979, 4745925, 4845303, 5025223, 5042331, 5049103, 5086663, 5162859, 5475373, 5510941, 5517849, 5646285, 5750739, 6033223, 6308343, 6358651, 6396291, 6431719, 6854983, 6870435, 6880111, 7041697, 7044289, 7097169, 7102173, 7331703, 7356265, 7430145, 7434021, 7496643, 7602349, 7712515, 7984863, 8036533, 8078925, 8150985, 8189923, 8206323, 8314165, 8350119, 8460349, 8477779, 8513935, 8564655, 8739085, 8785269, 9008209, 9009819, 9139815, 9236929, 9361651, 9435853, 9534301, 9569169, 9661771, 9930265] Harvey563 |
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