20190613, 13:08  #287 
Nov 2016
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20190618, 15:18  #288 
Nov 2016
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20190622, 09:24  #289 
Nov 2016
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20190624, 23:14  #290 
Nov 2016
2^{4}·157 Posts 
extended to the composite odd n, consider the numbers Phi(n,2) and Phi(2*n,2)
in the original new mersenne conjecture, it only consider the numbers 2^n1 and (2^n+1)/3 for prime odd n conjectures: * 127 is the largest number such that all three statements are true. * 345 is the largest number such that two of the three statements are true. Last fiddled with by sweety439 on 20190624 at 23:19 
20190625, 19:57  #291 
Nov 2016
2^{4}×157 Posts 
other conjectures:
* Phi_{Phi_n(2)}(2) is prime only for n = 2, 3, 4, 5, 6, 7, 8, 12 * Phi_{2*Phi_n(2)}(2) is prime only for n = 2, 3, 4, 5, 6, 7, 8, 10, 12, 14 this implies that there are no double mersenne primes > M(M7) = M(127) and no double wagstaff primes > W(W7) = W(43) a weaker conjecture: if Phi_n(2) is composite, then Phi_{Phi_n(2)}(2) and Phi_{2*Phi_n(2)}(2) are also composite Last fiddled with by sweety439 on 20190625 at 20:01 
20190629, 10:53  #292 
Nov 2016
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20190710, 23:43  #293 
Nov 2016
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20190710, 23:50  #294 
Nov 2016
2^{4}×157 Posts 
LYM does not exist for these (x,y) pairs:
* lcm(x,y) is divisible by 6 but neither x nor y is divisible by 6 * lcm(x,y) is divisible by 10 * (x, y) = (6, 9) In fact, the condition below is completely equivalent: (let val(n,k) be the highest power of k dividing n) * val(x,2) > val(y,2) but val(x,3) < val(y,3)  or  * val(x,2) < val(y,2) but val(x,3) > val(y,3) Thus, if at least one of x and y is 1, 5, 7 or E (i.e. coprime to 10), then this LYM must exist Last fiddled with by sweety439 on 20190711 at 00:04 
20190711, 21:26  #295 
Nov 2016
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20190712, 08:13  #296 
Nov 2016
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20190826, 16:05  #297 
Nov 2016
2^{4}×157 Posts 
Update the PARI program files.
