Lucky 13 (M51 related) - Page 23

BotXXX · 2019-01-03, 10:17

Congratulations!

M51 · 2019-01-03, 18:13

https://www.theregister.co.uk/2019/0..._prime_number/

LaurV · 2019-01-04, 05:44

Quote:

The new addition, named M82589933, belongs to a special class of prime numbers known for being particularly large.

Grrr... wooden tongue... (even for a non-native English speaker, like me). Good point the fact that points to the official release, tho..

Uncwilly · 2019-01-04, 15:15

The new accounts per day has been having some wild gyrations of late:
https://www.mersenne.org/primenet/graphs.php

Everytime a new article hits it must be making a difference.

philmoore · 2019-01-04, 22:06

Can anyone explain to me why this thread is titled "Lucky 13"?

I would also like to point out the significance of the fact that George Woltman and GIMPS have now discovered 1/3 of the known Mersenne primes. Extending the number of known Mersenne primes (and known perfect numbers) by 50% has never before happened in recorded history. It may, however, have happened in pre-history by the person who came up with the perfect number definition in Euclid's Elements, Book 7 and the proof that, essentially, Mersenne primes generate perfect numbers at the end of Book 9. The first people who formulated the concept of prime number may have discovered that 3, 7, and 31 are all prime, but I believe that the unknown person who is responsible for the perfect number theory in Euclid is also the person who discovered the fact that 496 shared a property with the numbers 6 and 28. This property may have been noticed by Egyptian mathematicians working with fractions in the form that 1/2 + 1/3 + 1/6 = 1, and 1/2 + 1/4 + 1/7 + 1/14 + 1/28 = 1, but I think that the person who extended this property to 496 must have recognized the justification in a way similar to that in Book 9, Proposition 36.

GP2 · 2019-01-04, 22:25

Quote:

Originally Posted by philmoore

Can anyone explain to me why this thread is titled "Lucky 13"?

Explained here.

JeppeSN · 2019-01-06, 17:45

Quote:

Originally Posted by philmoore

Extending the number of known Mersenne primes (and known perfect numbers) by 50% has never before happened in recorded history.

However, Robinson (the first person to use a computer for the Mersenne search) extended the number of known Mersenne primes from 12 to 17 in just nine months (in 1952). GIMPS has used over 22 years to extend the Mersenne prime count by 50%, from 34 to 51. /JeppeSN

GP2 · 2019-01-06, 18:44

Quote:

Originally Posted by JeppeSN

However, Robinson (the first person to use a computer for the Mersenne search) extended the number of known Mersenne primes from 12 to 17 in just nine months (in 1952).

The gap from 127 to 521 (the exponent of Robinson's first prime) was a ratio of 4.10, which is the largest known. The people doing LL tests by hand hadn't gotten past 257, if I recall...

If we have a similar relative gap after M51, then M52 will be (521/127) * 82589933 = M338813819

Which is actually a prime exponent!

And a 100M-digit Mersenne number!!

But... it has factors.

But it has a twin prime exponent M338813821 !!

Which also has a factor.

Seriously... a storybook ending... the exponent at the exact indicated spot being not just a prime but a twin prime... all ruined by a few stupid factors.

The nearest actual candidates are M338813749 and M338813953.

LaurV · 2019-01-07, 06:17

Quote:

Originally Posted by GP2

Seriously... a storybook ending... the exponent at the exact indicated spot being not just a prime but a twin prime... all ruined by a few stupid factors.

Haha, this post is genius! We love it!

philmoore · 2019-01-08, 22:52

Just a correction: The first to search for Mersenne primes via computer was not Raphael Robinson in 1952, but rather the team of Max Newman and Alan Turing, using the University of Manchester Mark I computer in 1951 to search all exponents up to 609 without finding a new prime. Unfortunately, the available memory was not sufficient to test the next prime exponent 621, so they just missed making the first Mersenne prime discovery by computer!

GP2 · 2019-01-08, 23:01

Quote:

Originally Posted by philmoore

Just a correction: The first to search for Mersenne primes via computer was not Raphael Robinson in 1952, but rather the team of Max Newman and Alan Turing, using the University of Manchester Mark I computer in 1951 to search all exponents up to 609 without finding a new prime. Unfortunately, the available memory was not sufficient to test the next prime exponent 621, so they just missed making the first Mersenne prime discovery by computer!

That can't be right. Your numbers are off. The Mersenne primes in that section are 521 and 607.

I'm halfway to memorizing the complete list of Mersenne prime exponents. It's the new digits-of-pi.

2019-01-03, 18:13	#244
M51 Dec 2018 2 Posts	Another article https://www.theregister.co.uk/2019/0..._prime_number/

2019-01-04, 22:06	#247
philmoore "Phil" Sep 2002 Tracktown, U.S.A. 2×13×43 Posts	What's 13 got to do with it? Can anyone explain to me why this thread is titled "Lucky 13"? I would also like to point out the significance of the fact that George Woltman and GIMPS have now discovered 1/3 of the known Mersenne primes. Extending the number of known Mersenne primes (and known perfect numbers) by 50% has never before happened in recorded history. It may, however, have happened in pre-history by the person who came up with the perfect number definition in Euclid's Elements, Book 7 and the proof that, essentially, Mersenne primes generate perfect numbers at the end of Book 9. The first people who formulated the concept of prime number may have discovered that 3, 7, and 31 are all prime, but I believe that the unknown person who is responsible for the perfect number theory in Euclid is also the person who discovered the fact that 496 shared a property with the numbers 6 and 28. This property may have been noticed by Egyptian mathematicians working with fractions in the form that 1/2 + 1/3 + 1/6 = 1, and 1/2 + 1/4 + 1/7 + 1/14 + 1/28 = 1, but I think that the person who extended this property to 496 must have recognized the justification in a way similar to that in Book 9, Proposition 36.

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2019-01-03, 10:17	#243
BotXXX Aug 2003 Europe 2·97 Posts	Congratulations!

2019-01-04, 15:15	#246
Uncwilly 6809 > 6502 """"""""""""""""""" Aug 2003 101×103 Posts 10001111101011₂ Posts	The new accounts per day has been having some wild gyrations of late: https://www.mersenne.org/primenet/graphs.php Everytime a new article hits it must be making a difference.

2019-01-08, 22:52	#252
philmoore "Phil" Sep 2002 Tracktown, U.S.A. 2136₈ Posts	Just a correction: The first to search for Mersenne primes via computer was not Raphael Robinson in 1952, but rather the team of Max Newman and Alan Turing, using the University of Manchester Mark I computer in 1951 to search all exponents up to 609 without finding a new prime. Unfortunately, the available memory was not sufficient to test the next prime exponent 621, so they just missed making the first Mersenne prime discovery by computer!