Mersenne number factored (disbelievers are biting elbows) - Page 39

Batalov · 2018-04-05, 17:05

You are confusing the proof method (which you obviously have by definition for every number in the UTM database) and the "record" category.
The "record" category is only there to get the candidate submissions eligible for submission.

Adding "ECPP" tag to small numbers is in fact discouraged by the UTM admins.

GP2 · 2018-07-15, 18:01

The 324th fully-factored or probably-fully-factored Mersenne number with prime exponent (not including the Mersenne primes themselves) is M32611.

It hasn't been PRP tested on Primenet yet, but when I reported the new factor to Factordb, it displayed FF.

As always, the Primo certification can be done by whoever claims it first.

Edit: actually, the results.txt file reported "Cofactor is a probable prime!" as well. I should have checked that first.

Batalov · 2018-07-15, 18:46

Will do proof

EDIT: Finished, uploaded and reported with UTM code c90.

wedgingt · 2018-07-16, 05:44

My data has 286 prime exponent Mersenne numbers with prime or SPRP cofactors, which is a bit less, but I have a somewhat different definition of factors for Mersenne numbers than factordb.com uses.

The sprp.c program (in the mers package) pulls out all the algebraic factors and factors that are also factors of smaller Mersenne numbers, so I've even had a few cases where a Mersenne number is "completely factored" by my definition before a Mersenne number that factors it is completely factored.

The largest in my "completely factored" list are appended.

-- Will

M( 32531 )
M( 35339 )
M( 41263 )
M( 41521 )
M( 41681 )
M( 57131 )
M( 58199 )
M( 63703 )
M( 82939 )
M( 86137 )
M( 86371 )
M( 87691 )
M( 106391 )
M( 130439 )
M( 136883 )
M( 157457 )
M( 173867 )
M( 221509 )
M( 271211 )
M( 271549 )
M( 406583 )
M( 684127 )

GP2 · 2018-07-16, 14:14

For whatever reason, Factordb doesn't record PRPs above around 500k, and there is no way to report them. They list M488441 as fully factored but not M576551 or anything higher.

Your list is missing a number of recent discoveries, particularly at the high end. They are indicated in the bold links below.

However, new factors are continually being discovered for exponents of all sizes, each of which could potentially result in a new PRP. So to complete the list you also have to consider exponents smaller than 32531. For instance M2789 was fully factored a few months ago.

The full list is at http://www.mersenne.ca/prp.php, however unlike Factordb or your sourceforge file, only prime exponents are recorded. There are 324 entries. The ones above your threshold of 32531 are listed below:

32531
32611
35339
41263
41521
41681
53381
57131
58199
63703
82939
84211
86137
86371
87691
106391
130439
136883
151013
157457
173867
174533
175631
221509
270059
271211
271549
406583
432457
440399
488441
576551
611999
675977
684127
696343
750151
822971
1010623
1168183
1304983
1629469
1790743
2327417
3464473
4187251
4834891
5240707
7080247
7313983

GP2 · 2018-07-16, 14:30

Quote:

Originally Posted by wedgingt

The sprp.c program (in the mers package) pulls out all the algebraic factors and factors that are also factors of smaller Mersenne numbers, so I've even had a few cases where a Mersenne number is "completely factored" by my definition before a Mersenne number that factors it is completely factored.

This distinction isn't an issue for Mersenne numbers with prime exponents, since these cannot share factors with one another.

Batalov · 2018-07-16, 14:51

PRPtop has a subset of these, too: http://www.primenumbers.net/prptop/s...&action=Search
(this search result requires additional filtering before use)

GP2 · 2018-07-16, 15:28

Quote:

Originally Posted by Batalov

PRPtop has a subset of these, too: http://www.primenumbers.net/prptop/s...&action=Search
(this search result requires additional filtering before use)

Unfortunately that site no longer accepts new entries smaller than 30,000 digits, so more recent discoveries such as M53381 and M84211 are not listed.

It does include a handful of Mersenne numbers with non-prime exponents, but those all seem to be old discoveries from more than a decade ago.

Batalov · 2018-07-16, 18:52

Yes, indeed - there is a self-inflicted gap up to 30,000 decimal digits.

However, there is always a (very remote) chance that someone somewhere is still digging for unusual high PRPs (not to mention NooE) and would submit just to PRPtop. Who knows. I do cross-reference all sites every once in a while.

GP2 · 2018-10-12, 15:01

The 325th fully-factored or probably-fully-factored Mersenne number with prime exponent (not including the Mersenne primes themselves) is M51487.

The most recent factor was found by Niels_Mache_Nextcloud, and the PRP test was done by trebor.

It still hasn't received a second, verifying PRP test on Primenet, but FactorDB confirms it.

paulunderwood · 2018-10-12, 15:43

Quote:

Originally Posted by GP2

The 325th fully-factored or probably-fully-factored Mersenne number with prime exponent (not including the Mersenne primes themselves) is M51487.

The most recent factor was found by Niels_Mache_Nextcloud, and the PRP test was done by trebor.

It still hasn't received a second, verifying PRP test on Primenet, but FactorDB confirms it.

Code:

time ./pfgw64 -k -f0 -od -q"(2^51487-1)/57410994232247/17292148963401772464767849635553" | ../../coding/gwnum/hybrid - 1 2 51487 -1
                                               
Testing (x + 1)^(n + 1) == 2 + 3 (mod n, x^2 - 3*x + 1)...
Likely prime!

real	0m1.274s
user	0m1.332s
sys	0m0.008s

2018-07-15, 18:01	#420
GP2 Sep 2003 5×11×47 Posts	The 324th fully-factored or probably-fully-factored Mersenne number with prime exponent (not including the Mersenne primes themselves) is M32611. It hasn't been PRP tested on Primenet yet, but when I reported the new factor to Factordb, it displayed FF. As always, the Primo certification can be done by whoever claims it first. Edit: actually, the results.txt file reported "Cofactor is a probable prime!" as well. I should have checked that first. Last fiddled with by GP2 on 2018-07-15 at 18:06

2018-07-15, 18:46	#421
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 7·23·61 Posts	Will do proof EDIT: Finished, uploaded and reported with UTM code c90. Last fiddled with by Batalov on 2018-07-17 at 18:43 Reason: finished yesterday

2018-07-16, 14:14	#423
GP2 Sep 2003 5·11·47 Posts	For whatever reason, Factordb doesn't record PRPs above around 500k, and there is no way to report them. They list M488441 as fully factored but not M576551 or anything higher. Your list is missing a number of recent discoveries, particularly at the high end. They are indicated in the bold links below. However, new factors are continually being discovered for exponents of all sizes, each of which could potentially result in a new PRP. So to complete the list you also have to consider exponents smaller than 32531. For instance M2789 was fully factored a few months ago. The full list is at http://www.mersenne.ca/prp.php, however unlike Factordb or your sourceforge file, only prime exponents are recorded. There are 324 entries. The ones above your threshold of 32531 are listed below: 32531 32611 35339 41263 41521 41681 53381 57131 58199 63703 82939 84211 86137 86371 87691 106391 130439 136883 151013 157457 173867 174533 175631 221509 270059 271211 271549 406583 432457 440399 488441 576551 611999 675977 684127 696343 750151 822971 1010623 1168183 1304983 1629469 1790743 2327417 3464473 4187251 4834891 5240707 7080247 7313983 Last fiddled with by GP2 on 2018-07-16 at 14:15

Similar Threads
Thread	Thread Starter	Forum	Replies	Last Post
Smallest exponent for mersenne not-factored	preda	PrimeNet	10	2018-11-04 00:47
Largest Mersenne Number Fully Factored?	c10ck3r	Data	49	2017-12-10 19:39
Possibility of a Fully-Factored Number	Trejack	FactorDB	7	2016-05-14 05:38
Estimating the number of primes in a partially-factored number	CRGreathouse	Probability & Probabilistic Number Theory	15	2014-08-13 18:46
Number of distinct prime factors of a Double Mersenne number	aketilander	Operazione Doppi Mersennes	1	2012-11-09 21:16

2018-04-05, 17:05	#419
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 7×23×61 Posts	You are confusing the proof method (which you obviously have by definition for every number in the UTM database) and the "record" category. The "record" category is only there to get the candidate submissions eligible for submission. Adding "ECPP" tag to small numbers is in fact discouraged by the UTM admins.

2018-07-16, 05:44	#422
wedgingt "Will Edgington" Nov 2010 Utah, USA 2³×3 Posts	My data has 286 prime exponent Mersenne numbers with prime or SPRP cofactors, which is a bit less, but I have a somewhat different definition of factors for Mersenne numbers than factordb.com uses. The sprp.c program (in the mers package) pulls out all the algebraic factors and factors that are also factors of smaller Mersenne numbers, so I've even had a few cases where a Mersenne number is "completely factored" by my definition before a Mersenne number that factors it is completely factored. The largest in my "completely factored" list are appended. -- Will M( 32531 ) M( 35339 ) M( 41263 ) M( 41521 ) M( 41681 ) M( 57131 ) M( 58199 ) M( 63703 ) M( 82939 ) M( 86137 ) M( 86371 ) M( 87691 ) M( 106391 ) M( 130439 ) M( 136883 ) M( 157457 ) M( 173867 ) M( 221509 ) M( 271211 ) M( 271549 ) M( 406583 ) M( 684127 )

2018-07-16, 14:51	#425
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 7·23·61 Posts	PRPtop has a subset of these, too: http://www.primenumbers.net/prptop/s...&action=Search (this search result requires additional filtering before use)

2018-07-16, 18:52	#427
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 7×23×61 Posts	Yes, indeed - there is a self-inflicted gap up to 30,000 decimal digits. However, there is always a (very remote) chance that someone somewhere is still digging for unusual high PRPs (not to mention NooE) and would submit just to PRPtop. Who knows. I do cross-reference all sites every once in a while.

2018-10-12, 15:01	#428
GP2 Sep 2003 A19₁₆ Posts	The 325th fully-factored or probably-fully-factored Mersenne number with prime exponent (not including the Mersenne primes themselves) is M51487. The most recent factor was found by Niels_Mache_Nextcloud, and the PRP test was done by trebor. It still hasn't received a second, verifying PRP test on Primenet, but FactorDB confirms it.