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Forum: Homework Help 2021-04-09, 19:35
Replies: 42
Views: 8,566
Posted By CRGreathouse
Let s =...

Let s = 33765749444723236975938383549571694531728722961303548619829414070181324100 so your number is s^2 + 1.

Is there some special significance to s or s^2 + 1?
Forum: Factoring 2021-04-01, 14:25
Replies: 3
Views: 719
Posted By CRGreathouse
Yes, your users have too much flexibility. They...

Yes, your users have too much flexibility. They could generate numbers until they find one with enough small factors (< 30 digits) to make finding the big one easy.
Forum: Factoring 2021-04-01, 14:12
Replies: 3
Views: 719
Posted By CRGreathouse
If large enough quantum computers come to pass,...

If large enough quantum computers come to pass, then all numbers of a certain size will be easy to factor. This size will depend on various factors of the quantum computer, but in the worst case (for...
Forum: Computer Science & Computational Number Theory 2021-03-30, 01:59
Replies: 5
Views: 3,172
Posted By CRGreathouse
I believe they each verified this independently...

I believe they each verified this independently back in 2010 (maybe 2009). When I say "independently", I mean that they wrote software implementations independently of each other -- they used the...
Forum: YAFU 2021-03-24, 04:02
Replies: 62
Views: 37,987
Posted By CRGreathouse
But that would be a non-random way (admittedly,...

But that would be a non-random way (admittedly, one that would only allow a certain number of bits of non-randomness to be smuggled in), and I do doubt that this sort of trickery was used.
Forum: YAFU 2021-03-24, 00:43
Replies: 62
Views: 37,987
Posted By CRGreathouse
My feelings match Paul's.

My feelings match Paul's.
Forum: Lounge 2021-03-23, 18:37
Replies: 37
Views: 3,635
Posted By CRGreathouse
There are lots of synthetic nucleotides out there...

There are lots of synthetic nucleotides out there beyond the standard ones.
Forum: Science & Technology 2021-03-19, 19:49
Replies: 274
Views: 24,621
Posted By CRGreathouse
I had an extremely sore arm for ~48 hours after...

I had an extremely sore arm for ~48 hours after my first shot (Pfizer) and the same, but for less than a day, following the second shot. My wife, who got the same vaccine, was practically knocked out...
Forum: Hardware 2021-03-19, 03:25
Replies: 16
Views: 1,644
Posted By CRGreathouse
:goodposting: Benefits of ECC to the project...

:goodposting:

Benefits of ECC to the project are dramatically reduced thanks to GEC. It's great if you want it for some other purpose.
Forum: Miscellaneous Math 2021-03-18, 01:09
Replies: 14
Views: 3,521
Posted By CRGreathouse
I'm not sure exactly what you were trying to do,...

I'm not sure exactly what you were trying to do, but feel free to drop me a PM. I'm an Editor-in-Chief (and Trustee) at the OEIS. I don't know that there's anything useful we can do for you but I'd...
Forum: GpuOwl 2021-03-12, 19:26
Replies: 16
Views: 2,240
Posted By CRGreathouse
How much larger? (We can't see the settings.)

How much larger? (We can't see the settings.)
Forum: Miscellaneous Math 2021-03-04, 03:14
Replies: 15
Views: 1,630
Posted By CRGreathouse
There are \pi(10^7) - \pi(10^6) = 586,081 in...

There are \pi(10^7) - \pi(10^6) = 586,081 in total.
Forum: Factoring 2021-03-03, 19:08
Replies: 18
Views: 4,293
Posted By CRGreathouse
I think it's really exciting to see someone...

I think it's really exciting to see someone trying (slightly) new things in this space -- since the 90s all we've been doing is tweaking the number field sieve. But he's pretty straightforward about...
Forum: Information & Answers 2021-02-24, 20:24
Replies: 20
Views: 1,523
Posted By CRGreathouse
The answer isn't at all obvious from what you'd...

The answer isn't at all obvious from what you'd read there, so don't get down on yourself.

The way this project had run for a long time was that we'd first run a battery of preliminary tests --...
Forum: Software 2021-02-24, 05:17
Replies: 8
Views: 1,424
Posted By CRGreathouse
PARI/GP is good, and since PARI is a C library it...

PARI/GP is good, and since PARI is a C library it transitions well into that language for higher-performance computing when needed (you can use gp2c if you want to live in both worlds).
Forum: Miscellaneous Math 2021-02-19, 16:57
Replies: 72
Views: 5,646
Posted By CRGreathouse
See A109461 (https://oeis.org/A109461) and...

See A109461 (https://oeis.org/A109461) and Mersenne Primes: Early history (https://primes.utm.edu/mersenne/#hist).
Forum: Miscellaneous Math 2021-02-19, 15:50
Replies: 72
Views: 5,646
Posted By CRGreathouse
...but you don't know the 165-year-old...

...but you don't know the 165-year-old Lucas-Lehmer test. For comparison, this (http://www.idaillinois.org/digital/collection/stc/id/22/) is what cars looked like 165 years ago, and this...
Forum: Miscellaneous Math 2021-02-18, 13:51
Replies: 18
Views: 2,091
Posted By CRGreathouse
Given a Carmichael number N or a semiprime p*q,...

Given a Carmichael number N or a semiprime p*q, what code do you run against it, exactly? Surely you're not looping over possible a, that would take forever.
Forum: Miscellaneous Math 2021-02-18, 06:01
Replies: 1
Views: 348
Posted By CRGreathouse
They look... strangely non-quantum to me. Maybe...

They look... strangely non-quantum to me. Maybe QMC is quantum, though I've heard the term used for a classical algorithm (simulated quantum annealing (https://arxiv.org/abs/1601.03030)) as well....
Forum: Miscellaneous Math 2021-02-17, 19:14
Replies: 40
Views: 3,140
Posted By CRGreathouse
See also...

See also https://www.loc.gov/standards/iso639-2/php/code_list.php (you could get lost in the ISO 639 standard, but 639-2 is a non-overwhelming subset).
Forum: Miscellaneous Math 2021-01-29, 21:11
Replies: 40
Views: 3,140
Posted By CRGreathouse
There's a lot of knowledge here on these boards...

There's a lot of knowledge here on these boards on sieves and their implementation. But without more information I'm not sure anyone is going to go into that much more detail.
Forum: Miscellaneous Math 2021-01-29, 05:33
Replies: 40
Views: 3,140
Posted By CRGreathouse
Tell on, then! Why do you need to know? This...

Tell on, then! Why do you need to know? This should help us understand which sieves are applicable. For example, would you could the Brun sieve? Probably not, but without knowing what you're doing...
Forum: Miscellaneous Math 2021-01-28, 19:28
Replies: 40
Views: 3,140
Posted By CRGreathouse
The most recent sieve I know of (can do more than...

The most recent sieve I know of (can do more than just primes, for example, could do the mu function or factorizations) is Helfgott's sieve (https://arxiv.org/abs/1712.09130).
Forum: Miscellaneous Math 2021-01-27, 03:41
Replies: 4
Views: 845
Posted By CRGreathouse
I think that's the only pure, nontrivial...

I think that's the only pure, nontrivial alternating sequence in the OEIS at the moment. There are A062157, A105812, A117154, A165326, and A280560 which alternate after some finite prefix, and of...
Forum: Science & Technology 2020-12-29, 21:00
Replies: 274
Views: 24,621
Posted By CRGreathouse
I couldn't find anything on LitCovid or the...

I couldn't find anything on LitCovid or the BNT162b2 trial paper (NEJM).
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