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Message boards : AP26 - AP27 Search : Are AP's also prime finders?

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Message 117642 - Posted: 1 May 2018 | 9:06:17 UTC

What I mean is...

Is an AP just a group of already known primes that are 'discovered' to be an AP or are they one or two (or more) primes with an AP, the AP is continued forwards and backwards to see if other numbers in the AP are prime or not, thereby 'discovering' new primes as the continuation of the sequence?

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555*2^3563328+1 (PPS-MEGA)

and

58523466^131072+1 (GFN-17 MEGA)

Michael Goetz
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Message 117645 - Posted: 1 May 2018 | 11:43:57 UTC

It may be impossible to answer that question. The primes found in AP27 are very small, and nobody keeps records of primes of that size.
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Paul Underwood

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Message 117646 - Posted: 1 May 2018 | 12:34:33 UTC - in response to Message 117642.

What I mean is...

Is an AP just a group of already known primes that are 'discovered' to be an AP or are they one or two (or more) primes with an AP, the AP is continued forwards and backwards to see if other numbers in the AP are prime or not, thereby 'discovering' new primes as the continuation of the sequence?

Dr David Broadhurst used the top5000 primes to look for AP3s.

In my searches for mid-sized APs, I sieve a range, then PRP it, after detect APs in the range and finally extend APs found in the range.

dukebg
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Message 117649 - Posted: 1 May 2018 | 15:16:30 UTC

I'll put it this way: for primes found in the APs of PrimeGrid's AP26-27 search, nobody cares about their "discovery" because primes of this size (tiny) are trivial to generate. Your computer actually generates millions (underestimation) of them during the run of a single unit. Discarding them unless they formed an arithmetic progression.

It's like discovery values of the individual sand grains in the playground.

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Message 117663 - Posted: 1 May 2018 | 20:23:43 UTC - in response to Message 117645.

So there's no 'prime bible'? A definitive reference that keeps a list of all known primes???
____________

Tonight's lucky numbers are

555*2^3563328+1 (PPS-MEGA)

and

58523466^131072+1 (GFN-17 MEGA)

Michael Goetz
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Message 117664 - Posted: 1 May 2018 | 20:47:52 UTC - in response to Message 117663.

So there's no 'prime bible'? A definitive reference that keeps a list of all known primes???

Correct. Small prime numbers are very numerous and easy to generate. I think there's a list out there somewhere of the first one billion primes. And, of course, there's the Top 5000 Primes website. And numerous web pages around with more specific primes.

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Message 117667 - Posted: 1 May 2018 | 23:35:05 UTC - in response to Message 117664.

So at what number of decimal places do you/we start to keep a track of primes? and why that number?
____________

Tonight's lucky numbers are

555*2^3563328+1 (PPS-MEGA)

and

58523466^131072+1 (GFN-17 MEGA)

Michael Goetz
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Message 117669 - Posted: 2 May 2018 | 0:49:22 UTC - in response to Message 117667.

So at what number of decimal places do you/we start to keep a track of primes? and why that number?

PrimeGrid records all of its primes.

If you're asking about an outside entity, there's the Top 5000 Primes website which records... the top 5000 Primes. How many digits that is increases over time, of course. Right now it's between 400 thousand and 500 thousand digits.

AP sequences of a significant length, i.e., the number of terms in the AP and not the number of digits in the primes, are recorded at Jens Kruse Andersen's Primes in Arithmetic Progression Records page. Currently, significant means "AP26 or longer". Prior to January, it meant "AP25 or longer", and back in 2010, it meant "AP24 or longer". Over time, as computers get more powerful, what is considered worth recording increases. The primes themselves are very short, typically less than 20 digits in length.

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My lucky number is 75898524288+1

Message boards : AP26 - AP27 Search : Are AP's also prime finders?