20200529, 18:11  #1 
May 2020
1_{16} Posts 
I think I discovered new largest prime
2^283.243.137 − 1 I dont use any computer. I use my new formule pls check it. Thnk you for everything

20200529, 18:15  #2 
6809 > 6502
"""""""""""""""""""
Aug 2003
101×103 Posts
37·223 Posts 
That is not a prime number. For it to be a Mersenne Prime, the exponent mus be prime. Your's is not.
Edit to insert link: https://www.mersenne.ca/exponent/283243137 Last fiddled with by Uncwilly on 20200529 at 19:16 
20200529, 18:57  #3 
"Curtis"
Feb 2005
Riverside, CA
4,219 Posts 
Next time you think your formula found a prime, check it yourself the software is found at mersenne.org. That way you won't have to share credit with anyone else!

20200628, 14:34  #4 
"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest
4,093 Posts 
https://www.alpertron.com.ar/ECM.HTM: 283 243137 = 3 × 17 × 23 × 241469
Mersenne numbers with composite (factorable) exponents are never prime: https://www.mersenneforum.org/showpo...13&postcount=4 so we know that 2^{283243137}1 has several factors and is not prime. (OP may benefit from the beginning of the larger reference material at https://www.mersenneforum.org/showthread.php?t=24607) 
20200710, 08:29  #5 
Jun 2020
3·7 Posts 

20200714, 07:50  #6 
"Jeppe"
Jan 2016
Denmark
176_{8} Posts 
To make what everybody else said already, more explicit:
Your exponent 283243137 is divisible by 3. So 283243137 = 3*N. Then the number you propose, namely 2^283243137  1, is equal to 2^(3*N)  1 = (2^3)^N  1. And that will be divisible by 2^3  1 = 7. So the number you suggest, is divisible by 7 (because your exponent is divisible by 3). /JeppeSN 
20200714, 15:51  #7 
"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest
FFD_{16} Posts 
What formula?
The alleged prime 2^283243137  1 can easily be shown to be composite without using a computer or calculator. Sum the decimal digits of the exponent: 33. (Sometimes called "casting out nines") The digit sum is obviously divisible by 3. Any number 2^n1 where n= a x b is composite, is composite, and is a repdigit (number with repeating digits), with factors 2^a1 and 2^b1 easily visible when expressed in base 2^a and 2^b respectively. Consider 2^81 = 255 = 2^(2*4)1 2^21 = 3 = 255/85. 2^41 = 15 = 255/17. 2^41 = 15 = 2^21 * cofactor 5. For an exponent with 4 distinct prime factors, for example from the OP, 283243137: https://www.alpertron.com.ar/ECM.HTM: 283243137 = 3 × 17 × 23 × 241469 a=3 (repdigit 2^3  1 = 7's in base 2^3 = 8) b=17 (repdigit 2^17  1 = 131071's in base 2^17 = 131072) c=23 (repdigit 2^23  1 = 8388607's in base 2^23 = 8388608) d=241469 (repdigit 2^241469  1 in base 2^241469) The number has numerous factors (at least 14, as shown below), each of which corresponds to being able to express the number as a repdigit in some base 2^B where 2^B=factor+1. For an exponent with four distinct prime factors, a, b, c, d, there are unique factors as follows prime factors 2^a1 2^b1 2^c1 2^d1 composite factors 2^(ab)1 2^(ac)1 2^(ad)1 2^(bc)1 2^(bd)1 2^(cd)1 2^(abc)1 2^(abd)1 2^(bcd)1 There's also a cofactor, whatever 2^(abcd)1 / (2^a1) / (2^b1) / (2^c1) / (2^d1) is. Which may be prime or composite. 
20200714, 19:33  #8  
Nov 2016
2095_{10} Posts 
Quote:
Phi_n(2) is prime for n = 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 17, 19, 22, 24, 26, 27, 30, 31, 32, 33, 34, 38, 40, 42, 46, 49, 56, 61, 62, 65, 69, 77, 78, 80, 85, 86, 89, 90, 93, 98, 107, 120, 122, 126, 127, 129, 133, 145, 150, 158, 165, 170, 174, 184, 192, 195, 202, 208, 234, 254, 261, 280, 296, 312, 322, 334, 345, 366, 374, 382, 398, 410, 414, 425, 447, 471, 507, 521, 550, 567, 579, 590, 600, 607, 626, 690, 694, 712, 745, 795, 816, 897, 909, 954, 990, 1106, 1192, 1224, 1230, 1279, 1384, 1386, 1402, 1464, 1512, 1554, 1562, 1600, 1670, 1683, 1727, 1781, 1834, 1904, 1990, 1992, 2008, 2037, 2203, 2281, 2298, 2353, 2406, 2456, 2499, 2536, ... Last fiddled with by sweety439 on 20200714 at 19:34 

20200714, 20:06  #9 
6809 > 6502
"""""""""""""""""""
Aug 2003
101×103 Posts
8251_{10} Posts 
OP never replied. Let's stop beating this horse. It has passed on.
Closing thread. 
Thread Tools  
Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
NEW MERSENNE PRIME! LARGEST PRIME NUMBER DISCOVERED!  dabaichi  News  561  20130329 16:55 
New prime discovered  kgr  Miscellaneous Math  3  20130304 09:20 
8th SoBprime discovered  27653  Frodo42  Lounge  1  20050615 19:44 
A new Sierpinski prime discovered!  gbvalor  Math  1  20021210 04:11 
need Pentium 4s for 5th largest prime search (largest proth)  wfgarnett3  Lounge  7  20021125 06:34 