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Forum: Miscellaneous Math 2020-09-21, 07:11
Replies: 9
Views: 381
Posted By JeppeSN
Red face I see an easy factorization of 2^n - 1 by...

I see an easy factorization of 2^n - 1 by induction: Suppose 2^(n-1) - 1 is factored. Then the factorization of 2^n - 2 is trivial. If we could somehow get the factorization from 2^n - 1 from that,...
Forum: Miscellaneous Math 2020-09-13, 09:34
Replies: 8
Views: 353
Posted By JeppeSN
Question How? For example, 7 divides 70, but s(7) = 2*7^2...

How? For example, 7 divides 70, but s(7) = 2*7^2 - 1 = 97 does not divide s(70) = 2*70^2 - 1 = 9799. Clearly enough, 97 divides 9797, hence 97 leaves a remainder of 2 when dividing into 9799?

It...
Forum: Information & Answers 2020-09-08, 08:09
Replies: 4
Views: 337
Posted By JeppeSN
16777216 = 2^24. Note that 2^16777216 + 1 =...

16777216 = 2^24.

Note that 2^16777216 + 1 = F(24) is the 24th Fermat number. No factors are known. You are probably searching for one.

However M(16777216) = 2^16777216 - 1 =...
Forum: Math 2020-09-02, 10:40
Replies: 3
Views: 1,373
Posted By JeppeSN
I wrote that OEIS entry. Did you ever complete...

I wrote that OEIS entry. Did you ever complete that ABC file to 2976221 or beyond? /JeppeSN
Forum: FactorDB 2020-09-01, 11:43
Replies: 3
Views: 338
Posted By JeppeSN
There must be or have been some inconsistence on...

There must be or have been some inconsistence on how the precedence is when the parentheses are not explicit.

If you type (10^79-181)%((10^79-1)/9) you come to the fully factored 79-digit...
Forum: Proth Prime Search 2020-09-01, 08:44
Replies: 25
Views: 3,475
Posted By JeppeSN
One reason for doing very tiny k is that they are...

One reason for doing very tiny k is that they are aesthetically more pleasing. Another reason is that the probability that each prime you find, will divide a Fermat number or a generalized Fermat...
Forum: Information & Answers 2020-08-17, 21:32
Replies: 38
Views: 6,857
Posted By JeppeSN
There are infinitely many primes of the form 4*x...

There are infinitely many primes of the form 4*x + 1. (https://math.stackexchange.com/questions/244915/) (This is more elementary than the more general Dirichlet theorem on arithmetic progressions...
Forum: Combinatorics & Combinatorial Number Theory 2020-08-17, 20:49
Replies: 5
Views: 887
Posted By JeppeSN
Red face Oops, that is right. It should have been 2^n-2...

Oops, that is right. It should have been 2^n-2 for n prime (http://factordb.com/index.php?query=2%5En-2&use=n&n=2&VP=on&EV=on&OD=on&PR=on&FF=on&PRP=on&CF=on&U=on&C=on&perpage=200&format=1&sent=Show),...
Forum: XYYXF Project 2020-08-17, 09:26
Replies: 2
Views: 262
Posted By JeppeSN
Lightbulb Thanks, that sounds like the explanation! So...

Thanks, that sounds like the explanation!

So it is n^k + k^n where either 1 < k ≤ n or 1 = k = n-1.

It is not really important if we include that exceptional case, or not.

There are similar...
Forum: Math 2020-08-17, 09:00
Replies: 6
Views: 608
Posted By JeppeSN
If I understand correctly, this PARI method...

If I understand correctly, this PARI method implements it:
LLFermat(m) = v=Mod(5,2^(2^m)+1);for(i=1,2^m-2,v=v^2-2);v==0
The way I understand Pépin's test, is:
Pepin(m) =...
Forum: XYYXF Project 2020-08-16, 11:58
Replies: 2
Views: 262
Posted By JeppeSN
Question 3 as Leyland prime?

Sorry if this has been asked before.

OEIS has the following two sequences:

(A076980) Leyland numbers: 3, together with numbers expressible as n^k + k^n nontrivially, i.e., n,k > 1 (to avoid n =...
Forum: PARI/GP 2020-08-16, 11:02
Replies: 13
Views: 940
Posted By JeppeSN
Angry I thought the problem would go away if you...

I thought the problem would go away if you shifted away from zero (where the floating point number representation can shift almost arbitrarily), but it still cannot do any of:
solve(x=-1, 2, x^3)...
Forum: Combinatorics & Combinatorial Number Theory 2020-08-16, 10:34
Replies: 5
Views: 887
Posted By JeppeSN
Agree with Batalov; for proving primality of M_p,...

Agree with Batalov; for proving primality of M_p, since the full factorization of M_p + 1 is trivial, we do not gain anything from the factorization of M_p - 1.

Of course, it may be fun to find...
Forum: Conjectures 'R Us 2020-08-05, 17:17
Replies: 78
Views: 14,709
Posted By JeppeSN
Smile Thank you for all the work you did on these two...

Thank you for all the work you did on these two k! I will write a post in this forum if a prime is ever located in one of these two series. /JeppeSN
Forum: Conjectures 'R Us 2020-08-05, 17:12
Replies: 7
Views: 967
Posted By JeppeSN
Thumbs up That private BOINC server now uses the residues...

That private BOINC server now uses the residues from CRUS for these two k, and double checks your work. And it has a status page now:...
Forum: Miscellaneous Math 2020-08-04, 15:52
Replies: 26
Views: 1,298
Posted By JeppeSN
You consider d(N) as the difference between the...

You consider d(N) as the difference between the number of odd natural numbers under N and the number of even natural numbers under N. Then d(N) does not converge for N tending to infinity, in the...
Forum: Miscellaneous Math 2020-08-04, 01:06
Replies: 26
Views: 1,298
Posted By JeppeSN
I do see some correct statements above. They...

I do see some correct statements above. They should be moved out of this crackpot subforum, by someone. Am I being trolled? /JeppeSN
Forum: Number Theory Discussion Group 2020-08-03, 18:13
Replies: 13
Views: 1,085
Posted By JeppeSN
That is true: This PARI/GP function imitates your...

That is true: This PARI/GP function imitates your program, with an optional seed argument:
findPeriod(p,seed=4)=s=Mod(seed,2^p-1);for(i=1,120000,s=s^2-2);S=s;i=0;until(s==S,S=S^2-2;i++);i
...
Forum: Number Theory Discussion Group 2020-08-03, 17:30
Replies: 13
Views: 1,085
Posted By JeppeSN
It is perhaps also interesting to note the...

It is perhaps also interesting to note the lengths of the "pre-periods", or offsets. That is the number of terms in the LL sequence preceding the first occurrence of the period. With Batalov's data...
Forum: Number Theory Discussion Group 2020-08-03, 07:33
Replies: 13
Views: 1,085
Posted By JeppeSN
Thumbs up Thanks, Batalov, that confirms my suspicion. For...

Thanks, Batalov, that confirms my suspicion. For example for p=37 (the first one Viliam Furik's method failed for), we start with:

4 -> 14 -> 194 -> 37634 -> 1416317954 -> (period starts here)...
Forum: Number Theory Discussion Group 2020-08-02, 09:26
Replies: 13
Views: 1,085
Posted By JeppeSN
Cool The LL sequence starts 4, 14, 194, ... Since...

The LL sequence starts 4, 14, 194, ...

Since we calculate modulo 2^p - 1, there are only finitely many values we can hit, so sooner or later we are going to hit a value we have seen before.

For...
Forum: Miscellaneous Math 2020-08-02, 01:02
Replies: 46
Views: 2,958
Posted By JeppeSN
Cool. The next one can be relevant for the Top...

Cool. The next one can be relevant for the Top 5000 of the Prime Pages (Caldwell). /JeppeSN
Forum: Math 2020-07-30, 08:35
Replies: 23
Views: 1,533
Posted By JeppeSN
For the LCM, with PARI, using...

For the LCM, with PARI, using lcm(apply(x->x-1,primes([3,23]))), you get 7920.

When you try to find the member from 2^1, 2^2, 2^3, ..., 2^7920 (mod 23#) with the least hammingweight, then nothing...
Forum: Math 2020-07-29, 19:06
Replies: 23
Views: 1,533
Posted By JeppeSN
An improvement (i.e. lower hammingweight) I can...

An improvement (i.e. lower hammingweight) I can get with that method, is the multiple 2^2513+1098793. It has pops 8. It is a multiple of 23# / 2. /JeppeSN
Forum: Math 2020-07-29, 18:42
Replies: 23
Views: 1,533
Posted By JeppeSN
Question I try the first one. With PARI/GP, I try znlog(j,...

I try the first one. With PARI/GP, I try znlog(j, Mod(2, 3 * 5 * 7 * 11 * 13 * 17 * 19 * 23)) for all j = -1, -2, -3, ... The first time it gives anything, is for j = -69613. Then my multiple is...
Showing results 1 to 25 of 155

 
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