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Old 2019-06-13, 13:08   #287
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Old 2019-06-18, 15:18   #288
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Old 2019-06-22, 09:24   #289
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Old 2019-06-24, 23:14   #290
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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^n-1 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.
Attached Files
File Type: txt new mersenne conjecture.txt (27.5 KB, 19 views)
File Type: txt numbers in new mersenne conjecture.txt (38 Bytes, 18 views)
File Type: txt counterexample for new mersenne conjecture.txt (33 Bytes, 18 views)

Last fiddled with by sweety439 on 2019-06-24 at 23:19
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Old 2019-06-25, 19:57   #291
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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 2019-06-25 at 20:01
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Old 2019-06-29, 10:53   #292
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Old 2019-07-10, 23:43   #293
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Old 2019-07-10, 23:50   #294
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Quote:
Originally Posted by sweety439 View Post
.........
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 2019-07-11 at 00:04
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Old 2019-07-11, 21:26   #295
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.......
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File Type: txt smallest alternating multiple of n.txt (15.3 KB, 16 views)
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Old 2019-07-12, 08:13   #296
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Old 2019-08-26, 16:05   #297
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Update the PARI program files.
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