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2019-06-13, 13:08   #287
sweety439

Nov 2016

1001110100002 Posts

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Attached Files
 least base such that smallest pseudoprime is n.txt (11.4 KB, 35 views)

2019-06-18, 15:18   #288
sweety439

Nov 2016

24·157 Posts

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Attached Files
 first prime value of Phi(n,x).txt (113.9 KB, 32 views)

2019-06-22, 09:24   #289
sweety439

Nov 2016

1001110100002 Posts

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Attached Files
 least prime power k such that n+k is also prime power.txt (32.4 KB, 21 views)

2019-06-24, 23:14   #290
sweety439

Nov 2016

24·157 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^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
 new mersenne conjecture.txt (27.5 KB, 22 views) numbers in new mersenne conjecture.txt (38 Bytes, 23 views) counterexample for new mersenne conjecture.txt (33 Bytes, 21 views)

Last fiddled with by sweety439 on 2019-06-24 at 23:19

 2019-06-25, 19:57 #291 sweety439     Nov 2016 24×157 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 2019-06-25 at 20:01
2019-06-29, 10:53   #292
sweety439

Nov 2016

1001110100002 Posts

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Attached Files
 least n such that k2^n-1 or k2^n+1 is prime.txt (31.0 KB, 20 views) record for the least n such that k2^n-1 or k2^n+1 is prime.txt (165 Bytes, 21 views)

2019-07-10, 23:43   #293
sweety439

Nov 2016

1001110100002 Posts

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Attached Files
 LYM.txt (496 Bytes, 19 views)

2019-07-10, 23:50   #294
sweety439

Nov 2016

24×157 Posts

Quote:
 Originally Posted by sweety439 .........
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

2019-07-11, 21:26   #295
sweety439

Nov 2016

24×157 Posts

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Attached Files
 least k such that nk is alternating.txt (11.5 KB, 20 views) smallest alternating multiple of n.txt (15.3 KB, 21 views)

2019-07-12, 08:13   #296
sweety439

Nov 2016

47208 Posts

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Attached Files
 smallest prime with digit sum n.txt (802 Bytes, 18 views)

2019-08-26, 16:05   #297
sweety439

Nov 2016

24×157 Posts

Update the PARI program files.
Attached Files
 program of permutable prime up to base 72.txt (1.2 KB, 14 views) program of permutable prime up to base 72 (written in base b).txt (1.3 KB, 14 views) program of minimal prime.txt (335 Bytes, 12 views) program of minimal prime (written in base b).txt (467 Bytes, 13 views)