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Forum: Miscellaneous Math 2020-09-22, 18:09
Replies: 40
Views: 1,322
Posted By CRGreathouse
It takes me > 10 minutes to test the composites...

It takes me > 10 minutes to test the composites up to 3000. :blush: Perhaps someone else can do better.

th2(p)=my(u='u,b=(Mod([1,1;1,u],p)^p)[1,2]); b==subst(b,u,p-u+2)
Forum: Analysis & Analytic Number Theory 2020-09-22, 14:21
Replies: 6
Views: 174
Posted By CRGreathouse
:bow:

:bow:
Forum: Alberico Lepore 2020-09-18, 17:58
Replies: 22
Views: 1,078
Posted By CRGreathouse
Sure, if you have enough information about the...

Sure, if you have enough information about the factor. If you don't know anything about the factors then it's much slower than other methods.
Forum: Prime Gap Searches 2020-09-18, 17:48
Replies: 82
Views: 9,107
Posted By CRGreathouse
I wouldn't say that, but I don't really...

I wouldn't say that, but I don't really understand what you're trying for here. The point of the paper was to give a heuristic which significantly improves upon Cramer; why would you analyze it with...
Forum: Miscellaneous Math 2020-09-17, 15:42
Replies: 40
Views: 1,322
Posted By CRGreathouse
Has anyone coded this in PARI/GP so we can test...

Has anyone coded this in PARI/GP so we can test various ranges?
Forum: Miscellaneous Math 2020-09-16, 19:18
Replies: 40
Views: 1,322
Posted By CRGreathouse
This sounds very much like a pseudoprime test, if...

This sounds very much like a pseudoprime test, if I understand your English.
Forum: Factoring 2020-09-16, 14:34
Replies: 6
Views: 262
Posted By CRGreathouse
:goodposting:

:goodposting:
Forum: Miscellaneous Math 2020-09-16, 03:25
Replies: 40
Views: 1,322
Posted By CRGreathouse
I'm not sure what there is to understand. You...

I'm not sure what there is to understand. You posted a test which looked like a probable prime test. On examination, it seems like primes pass it, most composites fail, and some composites pass. This...
Forum: Factoring 2020-09-16, 03:19
Replies: 7
Views: 253
Posted By CRGreathouse
It does act, in many ways, like a random...

It does act, in many ways, like a random algorithm. (In fact, the paper introducing it described it as a Monte Carlo method.) But as LaurV said, it is in fact completely deterministic.
Forum: Lounge 2020-09-15, 03:33
Replies: 1,071
Views: 46,537
Posted By CRGreathouse
It's a Hobson's choice: take the precautions,...

It's a Hobson's choice: take the precautions, save lives, and take a hit to the economy, or else fail to take precautions, people die, and the economy takes a hit anyway.
Forum: Lounge 2020-09-15, 01:11
Replies: 1,071
Views: 46,537
Posted By CRGreathouse
There's definitely cross-reactivity from various...

There's definitely cross-reactivity from various cornaviruses, I wouldn't say cross-immunity. I don't know the particular paper you're referencing, though.



Given that COVID-19 causes...
Forum: Lounge 2020-09-14, 19:01
Replies: 1,071
Views: 46,537
Posted By CRGreathouse
I haven't seen evidence of that, but that sounds...

I haven't seen evidence of that, but that sounds pretty exciting.
Forum: Lounge 2020-09-14, 17:15
Replies: 1,071
Views: 46,537
Posted By CRGreathouse
I definitely agree that the programs have...

I definitely agree that the programs have disincentivized work, and may continue to do so. There have been plenty of articles about people being angry at their small business owners for applying for...
Forum: Miscellaneous Math 2020-09-13, 06:12
Replies: 8
Views: 352
Posted By CRGreathouse
In that case, I don't find any examples below the...

In that case, I don't find any examples below the unfactored composite Mp = 2^1213 - 1.
Forum: Miscellaneous Math 2020-09-13, 04:04
Replies: 3
Views: 179
Posted By CRGreathouse
What are you taking the log of? If it's just the...

What are you taking the log of? If it's just the zeta, I don't get convergence. If it's the whole inner sum, what branch are you taking?
Forum: Miscellaneous Math 2020-09-13, 02:05
Replies: 8
Views: 352
Posted By CRGreathouse
2*2^2-1 | 2^3-1

2*2^2-1 | 2^3-1
Forum: Alberico Lepore 2020-09-10, 00:47
Replies: 22
Views: 1,078
Posted By CRGreathouse
[$]ab \equiv 1 \pmod4,[/$] so either [$]a \equiv...

[$]ab \equiv 1 \pmod4,[/$] so either [$]a \equiv b \equiv 1 \pmod4[/$] or [$]a \equiv b \equiv 3 \pmod4[/$].



[$$]2ab + 2a^2 + (b^2 - 2ab + a^2)/4 = (9a^2 + 6ab + b^2)/4[/$$]

Yep, this...
Forum: Miscellaneous Math 2020-09-09, 04:02
Replies: 3
Views: 228
Posted By CRGreathouse
I believe the first prime p for which all three...

I believe the first prime p for which all three numbers are not only composite, but for which all numbers within 100 of each are composite is p = 64516043. I imagine these primes should have density...
Forum: Information & Answers 2020-09-07, 02:44
Replies: 38
Views: 6,851
Posted By CRGreathouse
Alternate construction: by Bertrand's postulate...

Alternate construction: by Bertrand's postulate (proven by Chebyshev, re-proven by Ramanujan and many others), there is a prime between every two Mersenne numbers.
Forum: Alberico Lepore 2020-09-06, 00:19
Replies: 15
Views: 676
Posted By CRGreathouse
I hope you and your family are well. Take as long...

I hope you and your family are well. Take as long as you need.
Forum: Alberico Lepore 2020-09-05, 05:13
Replies: 15
Views: 676
Posted By CRGreathouse
18-digit factorization challenge

In another thread, Alberico Lepore posted:



I generated a random "hard" 59-bit semiprime for you:
390644893234047643
with the code
rsp...
Forum: jwaltos 2020-09-05, 02:35
Replies: 3
Views: 488
Posted By CRGreathouse
One example is the general concept of allometric...

One example is the general concept of allometric scaling, which seems to often take on rational exponents with small numerator and denominator like 3/2. See for example:...
Forum: enzocreti 2020-09-02, 03:32
Replies: 3
Views: 283
Posted By CRGreathouse
The first few terms are: 5, 8, 10, 13, 20, 24,...

The first few terms are: 5, 8, 10, 13, 20, 24, 26, 34, 59, 392.

392! - 1 = 78958785391722157 * P832.
392! + 1 = 32749 * P844.
Forum: Puzzles 2020-09-01, 14:28
Replies: 20
Views: 940
Posted By CRGreathouse
Oh right, of course. :blush:

Oh right, of course. :blush:
Forum: enzocreti 2020-08-31, 17:36
Replies: 20
Views: 423
Posted By CRGreathouse
I agree that 69660 == chinese([Mod(215,323),...

I agree that 69660 == chinese([Mod(215,323), Mod(0,215), Mod(6,13)]), and I'm prepared to assume that Pg(69660) is prime. But why should that make us think that
...
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