mersenneforum.org  

Go Back   mersenneforum.org > Extra Stuff > Blogorrhea > sweety439

Reply
 
Thread Tools
Old 2019-06-13, 13:08   #287
sweety439
 
sweety439's Avatar
 
Nov 2016

1001110100002 Posts
Default

............
Attached Files
File Type: txt least base such that smallest pseudoprime is n.txt (11.4 KB, 35 views)
sweety439 is offline   Reply With Quote
Old 2019-06-18, 15:18   #288
sweety439
 
sweety439's Avatar
 
Nov 2016

24·157 Posts
Default

............
Attached Files
File Type: txt first prime value of Phi(n,x).txt (113.9 KB, 32 views)
sweety439 is offline   Reply With Quote
Old 2019-06-22, 09:24   #289
sweety439
 
sweety439's Avatar
 
Nov 2016

1001110100002 Posts
Default

..............
sweety439 is offline   Reply With Quote
Old 2019-06-24, 23:14   #290
sweety439
 
sweety439's Avatar
 
Nov 2016

24·157 Posts
Default

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, 22 views)
File Type: txt numbers in new mersenne conjecture.txt (38 Bytes, 23 views)
File Type: txt counterexample for new mersenne conjecture.txt (33 Bytes, 21 views)

Last fiddled with by sweety439 on 2019-06-24 at 23:19
sweety439 is offline   Reply With Quote
Old 2019-06-25, 19:57   #291
sweety439
 
sweety439's Avatar
 
Nov 2016

24×157 Posts
Default

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
sweety439 is offline   Reply With Quote
Old 2019-06-29, 10:53   #292
sweety439
 
sweety439's Avatar
 
Nov 2016

1001110100002 Posts
Default

.....
sweety439 is offline   Reply With Quote
Old 2019-07-10, 23:43   #293
sweety439
 
sweety439's Avatar
 
Nov 2016

1001110100002 Posts
Default

.........
Attached Files
File Type: txt LYM.txt (496 Bytes, 19 views)
sweety439 is offline   Reply With Quote
Old 2019-07-10, 23:50   #294
sweety439
 
sweety439's Avatar
 
Nov 2016

24×157 Posts
Default

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
sweety439 is offline   Reply With Quote
Old 2019-07-11, 21:26   #295
sweety439
 
sweety439's Avatar
 
Nov 2016

24×157 Posts
Default

.......
Attached Files
File Type: txt least k such that nk is alternating.txt (11.5 KB, 20 views)
File Type: txt smallest alternating multiple of n.txt (15.3 KB, 21 views)
sweety439 is offline   Reply With Quote
Old 2019-07-12, 08:13   #296
sweety439
 
sweety439's Avatar
 
Nov 2016

47208 Posts
Default

........
Attached Files
File Type: txt smallest prime with digit sum n.txt (802 Bytes, 18 views)
sweety439 is offline   Reply With Quote
Old 2019-08-26, 16:05   #297
sweety439
 
sweety439's Avatar
 
Nov 2016

24×157 Posts
Default

Update the PARI program files.
sweety439 is offline   Reply With Quote
Reply

Thread Tools


All times are UTC. The time now is 21:36.

Mon Nov 30 21:36:32 UTC 2020 up 81 days, 18:47, 2 users, load averages: 2.30, 2.32, 2.34

Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2020, Jelsoft Enterprises Ltd.

This forum has received and complied with 0 (zero) government requests for information.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation.
A copy of the license is included in the FAQ.