20190623, 14:05  #298 
Nov 2016
4055_{8} Posts 
It seems that small factors of Phi_n(10) are searched for all n around 100000 and 200000, but small factors of Phi_n(2) are only searched by prime n and the n's which are power of 2, I know this project is searching this for n's which are twice an odd prime, bur how about other n? Is there anyone searching small factors of Phi_n(2) for all n around 100000 and 200000?

20190624, 04:52  #299 
Sep 2003
2,579 Posts 
The "factors of Phi_n(2) for n<=1280" file is subject to updates as new factors are found.
Because of the way OEIS handles files, every time the contents are updated, the link changes. The latest link is now _2.txt, which differs from _1.txt by having additional factors for exponents 991, 1213, 1219, 1261. 
20190624, 21:07  #300  
Nov 2016
7×13×23 Posts 
Quote:


20190625, 03:21  #301 
Sep 2003
2,579 Posts 

20190625, 16:56  #302 
Nov 2016
7×13×23 Posts 
However, you cannot enter "Phi_n(2)" in factordb, since factordb has no "cyclotomic polynomial" function, you can only enter "2^n1" (I know that 2^n1 = prod{dn}Phi_d(2))

20190628, 15:00  #303 
Sep 2003
5023_{8} Posts 
M1,073,741,827 has a factor: 16084529043983099051873383
This exponent is relevant to the (trivial) "New Mersenne Conjecture" 
20190629, 00:02  #304  
Nov 2016
4055_{8} Posts 
Quote:
Conjectures: * Phi(2^n1,2) is composite for all n>7 (it is prime for n = 2, 3, 4, 5, 7) * Phi(2^n+1,2) is composite for all n>7 (it is prime for all n <= 7) * Phi(2^n3,2) is composite for all n>6 (it is prime for n = 3, 4, 6) * Phi(2^n+3,2) is composite for all n>4 (it is prime for n = 1, 2, 4) * Phi(2*(2^n1),2) is composite for all n>7 (it is prime for all n <= 7) * Phi(2*(2^n+1),2) is composite for all n>4 (it is prime for n = 1, 2, 4) * Phi(2*(2^n3),2) is composite for all n>6 (it is prime for n = 2, 3, 4, 6) * Phi(2*(2^n+3),2) is composite for all n>4 (it is prime for n = 1, 2, 3, 4) * There are no odd n>345 such that both Phi(n,2) and Phi(2*n,2) are primes (there are both primes for n = 3, 5, 7, 13, 15, 17, 19, 31, 49, 61, 85, 127, 345, only consider odd n) * There are no odd n>345 such that both Phi(n,2)/gcd(Phi(n,2),n) and Phi(2*n,2)/gcd(Phi(2*n,2),n) are primes (there are both primes for n = 5, 7, 9, 13, 15, 17, 19, 21, 27, 31, 49, 61, 85, 127, 345, only consider odd n) Related to the New Mersenne Conjecture Last fiddled with by sweety439 on 20190629 at 00:22 

20190629, 00:11  #305 
Nov 2016
7×13×23 Posts 
The conjecture that there are only 5 Fermat primes is that there are no n>5 such that Phi(2^n,2) is prime, I conjectured that there are no n>7 such that Phi(2^n1,2) is prime, no n>7 such that Phi(2^n+1,2) is prime, no n>7 such that Phi(2*(2^n1),2) is prime, and no n>4 such that Phi(2*(2^n+1),2) is prime.
More generally, for every (positive or negative or zero, odd or even) integer k, there are only finitely many n such that 2^n+k is in OEIS A072226, i.e. there are only finitely many n such that Phi(2^n+k,2) is prime. Code:
k conjectured full list of such n 16 5, 15 5, 6, 14 4, 13 4, 5, 12 4, 11 4, 11, 10 4, 5, 9 4, 8 4, 5, 6, 7, 7 4, 6 3, 4, 5, 7, 5 3, 5, 9, 4 3, 4, 3 3, 4, 6, 2 2, 3, 4, 5, 6, 7, 8, 1 2, 3, 4, 5, 7, 0 1, 2, 3, 4, 5, 1 1, 2, 3, 4, 5, 6, 7, 2 1, 2, 3, 5, 3 1, 2, 4, 4 1, 2, 3, 5 1, 2, 3, 6, 7, 8, 6 1, 2, 3, 4, 5, 7 1, 3, 8 1, 2, 3, 4, 5, 9 2, 3, 9, 10 1, 2, 4, 5, 11 1, 2, 3, 4, 12 1, 2, 13 1, 2, 6, 14 1, 3, 4, 5, 6, 15 1, 2, 4, 16 3, 4, 6, Last fiddled with by sweety439 on 20190629 at 00:21 
20190701, 03:55  #306 
Jun 2003
4,637 Posts 
Code:
ECM found a factor in curve #8, stage #2 Sigma=5999343673417650, B1=50000, B2=5000000. 2^114743+1 has a factor: 363690536981293584763 (ECM curve 8, B1=50000, B2=5000000) 
20190701, 05:35  #307  
Sep 2002
Database er0rr
11×13×23 Posts 
Quote:
Code:
time echo 'print((2^114743+1)/3/565224019/581747011/601253321/810315067/69667542321371/7485151305966881/13863811976194993/363690536981293584763)'  gp q  ./bpsw2  1 2 114743 1 Testing (2*x)^((n + 1)/2) == 2 (mod n, x^2  9*x + 1)... Likely prime! real 0m8.926s user 0m8.980s sys 0m0.000s Last fiddled with by paulunderwood on 20190701 at 05:44 

20190701, 05:45  #308 
Jun 2003
4,637 Posts 
This would go as #2 on http://www.ellipsa.eu/public/primo/t...ml#PrimoRecord (if it were to be attempted).
How many core years do you estimate to prove this one? EDIT: Just missed paul's edit. The question still stands. Last fiddled with by axn on 20190701 at 05:46 
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