20200706, 18:22  #1  
Nov 2016
2,141 Posts 
Some other conjectures
Quote:
Also, how about test whether the numbers MW127 and WW127 is prime? (Wn = (2^n+1)/3) and other numbers like MW43, WW43, MM61, WM61, MW61, WW61? (MM43 and WM43 cannot be prime, since M43 is not prime, note that 127 is M7 and 43 is W7, and both M127 and W43 are primes) Last fiddled with by sweety439 on 20200706 at 18:23 

20200707, 00:43  #2  
"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest
3×11×127 Posts 
Quote:
Primality tests can not be performed on MM or MW or WW x where x > 32. The software does not exist, to my knowledge. (Mlucas ~MM32; gpuowl ~MM31; mprime ~MM30 for AVX512) The run times would be several years for gigadigit Mersennes or ~MM32, even on currently fastest available gpus. Required ram and permanent storage also impose limits, on both primality testing and P1 factoring, on gpus and cpus, estimated as less than MM37 and MM42 for current hardware feasible ram, and MM67 for existing file systems' capacity limits. https://www.mersenneforum.org/showpo...1&postcount=10 So I assume you mean how about heavily trial factor these. How many gpumonths or years are these worth? Last fiddled with by kriesel on 20200707 at 00:47 

20200707, 04:41  #3  
Nov 2016
2,141 Posts 
Quote:
Like the case of Fermat numbers: F0=3 is prime, F1=5 is prime, F2=17 is prime, F3=257 is prime, F4=65537 is prime, but F5=4294967297=641*6700417 is composite, and Fn is composite at least for 5<=n<=32 In the case of CatalanMersenne numbers: C0=2 is prime, C1=3 is prime, C2=7 is prime, C3=127 is prime, C4=170141183460469231731687303715884105727 is prime, but I think that C5 is composite, of course if C5 is composite, then Cn is composite for all n>=5 Fn = (F(n1)1)^2+1, F0 = 3 Cn = 2^C(n1)1, C0 = 2 There is another sequence highly related to these numbers, Double Mersenne numbers: Define Dn = MM(nth prime) D1=7 is prime, D2=127 is prime, D3=2147483647 is prime, D4=170141183460469231731687303715884105727 is prime, but Dn is composite at least for 5<=n<=17 I think that Fn, Cn, and Dn are primes only for n<=4, and composite for n>4 (think about that: polynomial equations with degree n have algebraic solution if and only if n<=4) Last fiddled with by sweety439 on 20200707 at 04:52 

20200707, 04:45  #4  
Nov 2016
2,141 Posts 
Quote:


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