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Forum: And now for something completely different 2021-04-21, 07:16
Replies: 65
Views: 7,304
Posted By JeppeSN
Good one! Maybe it will be clear when the...

Good one!

Maybe it will be clear when the PRP Top entry becomes visible, but what types of PRP tests has this one "passed", as of now?

/JeppeSN
Forum: Miscellaneous Math 2021-04-20, 14:03
Replies: 12
Views: 1,424
Posted By JeppeSN
I guess it is true that every odd factor of...

I guess it is true that every odd factor of Phi(n,b)/gcd(Phi(n,b),n) (with b≥2) (where Phi is the cyclotomic polynomial, and gcd is greatest common divisor) is of the form kn+1. /JeppeSN
Forum: Riesel Prime Search 2021-02-19, 08:48
Replies: 282
Views: 49,442
Posted By JeppeSN
Arrow This beats an idea of simply doing 10^999999 +...

This beats an idea of simply doing 10^999999 + k*10^(333333-m) ± 1 with m very small. Such a prime would be simpler to test than Serge Batalov's, but not quite as close to 10^999999. /JeppeSN
Forum: FermatSearch 2021-02-16, 12:31
Replies: 12
Sticky: gfn results
Views: 9,899
Posted By JeppeSN
I added the information to...

I added the information to https://primes.utm.edu/primes/page.php?id=131760#comments

It had already appeared on http://www.prothsearch.com/GFNfacs.html

/JeppeSN
Forum: Math 2021-01-18, 15:43
Replies: 8
Views: 1,559
Posted By JeppeSN
Thumbs down The official policy of OEIS disagrees. On...

The official policy of OEIS disagrees.

On https://oeis.org/SubmitB.html you can read:



So just because it is faster to calculate a sequence than to fetch it over the internet, does not mean...
Forum: FermatSearch 2021-01-17, 23:57
Replies: 339
Views: 80,482
Posted By JeppeSN
You may be aware that PrimeGrid found:...

You may be aware that PrimeGrid found: https://primes.utm.edu/primes/page.php?id=131583
27*2^7963247 + 1 divides Fermat F(7963245)
/JeppeSN
Forum: FermatSearch 2020-11-19, 10:33
Replies: 65
Views: 11,496
Posted By JeppeSN
Wink And the difference between F0 and pi is negative....

And the difference between F0 and pi is negative. /JeppeSN
Forum: FermatSearch 2020-11-19, 00:41
Replies: 65
Views: 11,496
Posted By JeppeSN
MM82589933 = 2^(2^82589933-1) - 1 is a prime. ...

MM82589933 = 2^(2^82589933-1) - 1 is a prime.

Now please prove me wrong - any prime factor of that number would be the largest prime ever found.

/JeppeSN
Forum: FermatSearch 2020-10-12, 22:20
Replies: 339
Views: 80,482
Posted By JeppeSN
Lightbulb But before that, Ravi Fernando showed me: ...

But before that, Ravi Fernando showed me:

Let p = k * 2^n + 1 be a prime that divides a Fermat number. From the formula, we can write k = -1/2^n (mod p). But the order of 2 (mod p) is a power of...
Forum: FermatSearch 2020-10-12, 20:10
Replies: 339
Views: 80,482
Posted By JeppeSN
Thumbs up Cool. It should be added as a User comment on...

Cool. It should be added as a User comment on https://primes.utm.edu/primes/page.php?id=131289. If you have at least one prime on primes.utm.edu, you can do it. Ask me if you do not know how to do...
Forum: FermatSearch 2020-10-11, 12:18
Replies: 339
Views: 80,482
Posted By JeppeSN
Thumbs up Very good. Thank you. So in this case the number...

Very good. Thank you. So in this case the number will be carefully checked and double checked. But I also wrote to Ryan P. to make sure future primes are not forgotten. /JeppeSN
Forum: FermatSearch 2020-10-10, 20:49
Replies: 339
Views: 80,482
Posted By JeppeSN
Dear rynp, Congratulations with this...

Dear rynp,

Congratulations with this remarkable discovery!

Has the above PFGW run completed by now? I see no User comment mentioning the GF(-, 7) divisor on...
Forum: Math 2020-10-06, 20:28
Replies: 5
Views: 2,073
Posted By JeppeSN
This part is explained in...

This part is explained in https://en.wikipedia.org/wiki/Second_Hardy%E2%80%93Littlewood_conjecture – if the First Hardy–Littlewood conjecture is true, then this implies that the second...
Forum: Miscellaneous Math 2020-09-21, 07:11
Replies: 9
Views: 2,969
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: 3,226
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: 2,585
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: 5,418
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: 4,825
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: 27
Views: 18,884
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: 20,867
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: 9
Views: 24,175
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: 4,869
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: 8
Views: 5,780
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: 4,869
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: 11,236
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)...
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