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-   -   Sierpinski/Riesel Base 5: Post Primes Here (https://www.mersenneforum.org/showthread.php?t=3125)

 robert44444uk 2004-09-28 22:48

Sierpinski/Riesel Base 5: Post Primes Here

I have been looking for the lowest Sierpinski and Riesel numbers base 5. In the y*hoo primeform group you will see posts about it.

The lowest even Reisel number is mooted to be 346802 and the lowest even Sierpinski 159986. That is to say 346802.5^n-1 is always composite for every n, and 159986.5^n+1 is similarly endowed.

The Sierpinskis look the easiest to look at. We have to show there is a prime for every even k (in the power series k.5^n+1) less than k=159986 and I have checked so far up to n=18468 for all of the remaining values of k shown below. All other values of k have a prime at less than n=18468

If anyone wants to take a stab at any of the values then reserve a k by answering this thread and run it up to a certain value of n, and post either the prp or the range tested.

As usual, I will not be able to take a terribly active role in all of this, I have no computer power and work takes up a lot of my time right now.

Regards to all of the mersenneforum

Robert Smith

[code]
2822
3706
4276
4738
5048
5114
5504
6082
6436
6772
7528
8644
9248
10918
12988
14110
15274
15506
15802
18530
21380
23690
24032
25240
25570
26798
27520
27676
29356
29914
30410
30658
31286
31712
32122
32180
32518
33358
33448
33526
33860
34094
36412
37246
37292
37328
37640
37714
37718
38084
40078
41738
42004
43018
43220
44134
44312
44348
44738
45652
45748
46240
46922
48424
49804
50192
51176
51208
51460
54590
55154
57316
58642
59302
59444
59912
60124
60394
60722
62698
64258
64940
66242
67282
67612
67748
68294
68416
68492
70550
71098
71492
74632
76246
76324
76370
76724
77072
77530
77908
78002
78398
79010
81556
81674
81700
82486
83032
83936
84032
84284
86354
89806
90056
90676
92158
92162
92182
92650
92906
93254
93374
93484
95246
96806
96994
98288
99784
99926
100898
101152
101284
102196
102482
104624
105166
105464
105754
106418
106588
106688
106900
107216
107258
108074
108308
109208
109988
110242
110488
110846
111382
111424
111502
111688
111994
113156
114158
117434
118388
118450
118568
120160
123406
123748
123910
125494
126134
126200
127312
127850
128432
128552
128896
129028
130324
131416
132028
133778
133990
135376
135526
136408
137132
137422
137600
137714
138022
138380
138514
138724
139196
139394
139606
139784
140498
141532
141578
143092
144052
144932
145982
146372
146780
149570
150506
150526
152050
152588
152836
153290
154222
156430
158044
158560
158696
159106
159128
159706
[/code]

 robert44444uk 2004-09-29 18:54

5 less to look for

89038*5^18576+1
79010*5^18901+1
15802*5^18902+1
106588*5^18920+1
82486*5^19224+1

 robert44444uk 2004-10-06 21:21

And more - 204 to go!

81700*5^20040+1
89806*5^20852+1
95246*5^21669+1
132028*5^21736+1
138022*5^22280+1
141532*5^22472+1

The size of these first-time prp numbers is getting interesting and only 204 candidates to check.

Regards

Robert Smith

 robert44444uk 2004-10-07 06:16

Sieve

Actually have not started sieving yet! Just pre factoring ( -f100) in pfgw. Populations of candidates with no factors under 1000000 are only 1-3% or so in any case.

Don't know of a quick way to sieve 200 candidates, Phil Carmody developed software to sieve 12 at a time.

But it would be easy to take a few candidates and sieve in NewPGen and run up to 200000 or so.

Regards

Robert Smith

PS: 150506*5^22667+1 popped up overnight

 ltd 2004-10-07 17:45

A first result using winpfgw (v1.2 rc1b)

159128*5^19709+1

Lars

 robert44444uk 2004-10-11 16:08

Some more

Lars and other interested folk:

I have been away for a few days, and the following are all first primes - sorry for the one over 150000, I shall stop testing these.

150506*5^22667+1
33860*5^23213+1
6772*5^23214+1
104624*5^23443+1
137714*5^23863+1
96806*5^24813+1
106418*5^25077+1
59302*5^25228+1

All remaining candidates are tested to n=25228. After these and Lars's discovery there are 195 remaining candidates.

I will take on the first 12 of the remainder and check to n=200000, namely

2822
3706
4276
4738
5048
5114
5504
6082
6436
7528
8644
9248

Regards

Robert Smith

 geoff 2004-10-27 11:13

I found the following two primes:

15274*5^31410+1
15506*5^39203+1

These four k have no primes for n < 50000:

10918
12988
14110
18530

I am going to stop there for now.

 geoff 2004-12-26 08:36

I found these two primes: 30658*5^29860+1, 31286*5^59705+1 (196 to go).

These two k have no primes for n < 60000, so I'm releasing them: 30410, 31712.

I'm reserving the following six k: 32122, 32180, 32518, 33358, 33448, 33526.

 ltd 2004-12-26 19:40

Hi,

finally there is a new report from my side.
I have checked my logs and found that i did forget to test k=153290 upto n=30000 and guess what i found:

153290*5^29859+1 is prime!!!!!

I keep my other k reserved.

Lars

 ltd 2005-01-02 08:36

OK here are the results from my search.

All k are tested to n=50000. I will unreserve these k for now.

And here comes the important part:

159706*5^35244+1 is prime
158044*5^43818+1 is prime

Lars

 Templus 2005-01-06 10:41

In the case that 21380*5^n+1 equals to 4276*5^(n+1)+1 , the following are prime:

4276*5^50626+1
21380*5^50625+1
106900*5^50624+1

Shouldn't we remove all multiples of 10 (which are multiples of 5) which have duplicate k's in the list? Like the k I mentioned above?

2822 / 14110 / 70550
18530 / 92650
4738 / 23690 / 118450
5114 / 25570 / 127850
5504 / 27520 / 137600
6082 / 30410 / 152050
6436 / 32180
6772 / 33860

And so on....The most left number is the 'base' number and the numbers following it are multiples of 5 of it. So why would we check for their primality, if we new the primality of a multiple of it?

Am I right? (Just a n00b on primality)

Also, I'm now reserving k = 24032 until n=100000

 Templus 2005-01-06 20:35

You're right Geoff.

I found a prime for 21380*5^50625+1 , which is equal to 4276*5^50626+1. But this doesn't mean that k=4276 doesn't have a prime for n less than 50626, so that's one thing that has to be checked!

 geoff 2005-01-06 21:22

[QUOTE=Templus]I found a prime for 21380*5^50625+1 , which is equal to 4276*5^50626+1. But this doesn't mean that k=4276 doesn't have a prime for n less than 50626, so that's one thing that has to be checked![/QUOTE]
Nice one!

It doesn't matter for the project whether or not k=4276 could have been eliminated by a smaller n than n=50626, any prime will do. The only problems are for k such as k=123910=5*24782. 24782 has already been eliminated because 24782*5^1+1 is prime, but this doesn't rule out the possibility that 123910*5^n+1 = 24782*5^(n+1)+1 is composite for all n. This means we have to leave k=123910 in the list.

 geoff 2005-01-06 22:08

OK the outcome of the observation by Templus is that all multiples of 5 can be eliminated except for 51460, 81700 and 123910, and Robert already found a prime for 81700. This means there are only 161 candidates left to test.

 robert44444uk 2005-01-07 19:39

Results

4276*5^50626+1
4738*5^41656+1
5048*5^37597+1
5504*5^39475+1

are all PRP3.

other checked to
2822 50057
3706 65328
5114 191771

Will now start on:

6082
6436
7528
8644
9248

Regards
Robert Smith

 geoff 2005-01-15 03:02

[QUOTE=Templus]Geoff, did you see that I reserved k = 24032 on the sixth of january?[/QUOTE]
Sorry I missed that, noted now.

My new results are: 33358*5^38096+1 and 33526*5^41142+1 are prime.

 robert44444uk 2005-01-15 12:27

Results to 10000

Searching for the remaining candidates k less than 10000 did not reveal any new prps:

K largest n checked
6082 77402
6436 61512
7528 90216
8644 79150
9248 85471

Regards

Robert Smith

 robert44444uk 2005-01-15 12:32

Reservations

Geoff

I will take candidates 110000-120000 next

Regards

Robert Smith

 robert44444uk 2005-01-17 21:03

Seriously big prime

[url]http://primes.utm.edu/primes/page.php?id=73175[/url]

Primality testing 111502*5^134008+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 11
Calling Brillhart-Lehmer-Selfridge with factored part 99.99%
111502*5^134008+1 is prime! (1503.0378s+0.0176s)

First prime I have found for a while. It will be the 1000 to 1100 range of largest primes ever found, tantalisingly close to 100000 digits.

Interestingly this is the k value which we might have expected to give the most problem having the smallest smallest Nash weight of all the remaining candidates!

Regards

Robert Smith

 michaf 2005-01-18 08:52

one down

Hi there,

My first prime for this project:

PFGW Version 20041020.Win_Stable (v1.2 RC1c) [FFT v23.8]

Primality testing 37246*5^50452+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 11
Running N-1 test using base 13
Calling Brillhart-Lehmer-Selfridge with factored part 99.99%
37246*5^50452+1 is prime! (456.9443s+0.0070s)

Cheers, Micha Fleuren

 michaf 2005-01-24 22:30

One more down

Hi all,

I got one more down today, finding my second prime:

PFGW Version 20041020.Win_Stable (v1.2 RC1c) [FFT v23.8]

Primality testing 38084*5^29705+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2
Calling Brillhart-Lehmer-Selfridge with factored part 99.98%
38084*5^29705+1 is prime! (65.7210s+0.0034s)

Cheers, Micha

 robert44444uk 2005-01-25 19:43

The Riesel base 5 series

I have taken a slight excursion away from Sierpinski base 5 to prepare the groundwork for the Riesel base 5 study. I have checked up to around n=12250 and I am still clearing 9-10 candidates a day. I will stop when sieving individual candidates makes sense. Right now there are 465 candidates left, so we should still work on the Sierpinski set.

For the Sierpinski series, I have checked the following k to the following n with no primes:
k n
110242 52766
110488 55772

And I have discovered:

111994 30446 is prp3

Regards

Robert Smith

 geoff 2005-01-25 22:11

Robert, could you make available a list of the primes you found for n <= 18468? Or if you email it to me ( geoff AT hisplace DOT co DOT nz ) I will make it available.

I will keep a list of primes that make the top 5000 list in [url]http://www.geocities.com/g_w_reynolds/Sierpinski5/champs.txt[/url], there is just one entry so far.

My results: I found (a while ago) that 32518*5^47330+1 is prime.
I am reserving these k: 10918, 12988, 31712.

 michaf 2005-01-28 06:31

Hello all,

I agree with uncwilly that this project should deserve it's
own private place... anyone know how to move it?

In the meantime:

One more down:

PFGW Version 20041020.Win_Stable (v1.2 RC1c) [FFT v23.8]

Primality testing 42004*5^27992+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2
Calling Brillhart-Lehmer-Selfridge with factored part 99.98%
42004*5^27992+1 is prime! (57.0569s+0.0044s)

 michaf 2005-01-30 12:42

Yet another one down

Hi all,

4th prime on here:

PFGW Version 20041020.Win_Stable (v1.2 RC1c) [FFT v23.8]

Primality testing 44134*5^39614+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 7
Calling Brillhart-Lehmer-Selfridge with factored part 99.98%
44134*5^39614+1 is prime! (150.2650s+0.0062s)

Cheers, Micha

 ltd 2005-01-31 20:28

Hi,

60124*5^38286+1 is prime!

60394 tested to 50166 ( i keep this reserved)
60722 tested to 49329 ( i keep this reserved)

I also keep my other k reserved.

Lars

 geoff 2005-02-01 02:13

The primes.txt file in [url]http://www.geocities.com/g_w_reynolds/Sierpinski5/[/url] contains the k,n pairs for all the primes k*5^n+1 found so far. It can be used as input to Proth.exe in file mode, or by adding 'ABC \$a*5^\$b+1' to the top, as input to pfgw.

 robert44444uk 2005-02-01 18:01

Nought

This may come to nought, actually no, it will come to k+1

What am I talking about? n=0 ---> k*5^0+1= k+1

Therefore any k still remaining where k+1 is prime can be eliminated, unless that is not in the Sierpinski rule book. Looking at my original list, this would eliminate 7528 and maybe others....not got a list of primes to hand

What does this group think of this wheeze?

Regards

Robert Smith

 robert44444uk 2005-02-01 21:09

n=0

Following on, now I am home:

From the original list n=0 eliminates (and a number of these we have found already higher primes or prp for):

7528
15802
33358
43018
51460
81700
82486
90676
102196
105166
123406
123910
143092
152836
159706

Regards

Robert Smith

 geoff 2005-02-01 22:35

[QUOTE=robert44444uk]Therefore any k still remaining where k+1 is prime can be eliminated, unless that is not in the Sierpinski rule book.[/QUOTE]
The definitions of Sierpinski number that I have seen take n to be positive, e.g. [url]http://mathworld.wolfram.com/SierpinskisCompositeNumberTheorem.html[/url], so I think we should leave these k in the list. (If they turn out to be harder than the other k then we could reconsider :-)

 pcco74 2005-02-02 14:01

[QUOTE=geoff]The definitions of Sierpinski number that I have seen take n to be positive, e.g. [url]http://mathworld.wolfram.com/SierpinskisCompositeNumberTheorem.html[/url], so I think we should leave these k in the list. (If they turn out to be harder than the other k then we could reconsider :-)[/QUOTE]
Yves Gallot's site also lists n as having to be greater than or equal to one. [url]http://www.prothsearch.net/sierp.html[/url]

 Citrix 2005-02-02 18:10

[QUOTE=pcco74]Yves Gallot's site also lists n as having to be greater than or equal to one. [url]http://www.prothsearch.net/sierp.html[/url][/QUOTE]

This is for base 2 only, 5^0 should be considered too.

 robert44444uk 2005-02-02 19:10

Odds and evens

I posted the following message on Yahoo primenumbers to see whether one of the maths bods can give an answer. I am reasonably confident we should allow n=0

Regards

Robert Smith

 pcco74 2005-02-02 19:43

The reason k must be odd for base 2 is that if k is even, you can always divide it by 2 until you get an odd k, and increase n accordingly. Ex. 10*2^2+1=5*2^3+1. This simply eliminates testing the same number multiple times, and provides for a common format for these numbers. As far as n=0, I really think this should not be included for the following two reasons. First, it is not included in the original Sierpinski numbers, which we are trying to represent in base 5. Second, including n=0 eliminates all information on the base. For example, 4*2^0+1=4*5^0+1=4*45569^0+1. This defeats the purpose by reducing the expression k*b^n+1 to the much more general form k+1, or basically k.

 rogue 2005-02-04 14:11

Update:

Primality testing 123910*5^136268+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 11
123910*5^136268+1 is prime! (1597.4078s+0.0268s)

Yes I know that Robert believes that we don't need to test this number, but as I had sieved fairly deeply and had already done so much PRP testing, I decided to continue knowing that if I found a prime it would be near 100000 digits. It is, at 95253 digits. It will be stored as 24782*5^136269+1 in Chris Caldwell's database.

109208 done to 188000 (still reserved)
71492 done to 55000 (still reserved)

 robert44444uk 2005-02-04 17:33

Wow

Rogue - many congrats are in order for finding such a large prime - all power to you.

Actually though, and I am being pedantic, it is the second prime for this value of k, the first being n=0, as is shown on Geoff's list 24782 when n=1 removed that number from checking.

But how nice to find a juicy big prime !!

Regards

Robert Smith

 michaf 2005-02-05 09:46

Delighted

Hello all,

After a delightfull stay in Disney Resort Paris,
I came home to a computer stating me a delightful find:

PFGW Version 20041020.Win_Stable (v1.2 RC1c) [FFT v23.8]

Primality testing 37718*5^104499+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 11
Calling Brillhart-Lehmer-Selfridge with factored part 99.99%
37718*5^104499+1 is prime! (1165.4437s+0.0267s)

Number was ranked 1737th largest prime ever yesterday evening

Cheers, Micha

 geoff 2005-02-06 03:39

Congratulations rogue and michaf for the big primes.

If n=0 is allowed in the definition of base-5 Sierpinski number, then k=7528 has a prime 7528*5^0+1, but we will still need to eliminate k=5*7528=37640, so a prime 7528*5^n+1 for n >=1 must be found either way. This is the only exceptional case in Roberts list above, I have added an asterisk beside the other candidates in status.txt that don't need to be tested if n=0 is allowed.

My own results:
83032*5^39408+1 is prime.
33448*5^n+1 is not prime for n <= 100,000 and I am releasing it.

 ltd 2005-02-06 11:06

One more down.

67282*5^45336+1 is prime.

Lars

 ltd 2005-02-08 19:46

And the next result:

68294*5^33723+1 is prime!

I keep the rest of my ranges reserved.

Lars

 michaf 2005-02-11 18:10

six down for me now

Hya's

found myself my sixth prime:

PFGW Version 20041020.Win_Stable (v1.2 RC1c) [FFT v23.8]

Primality testing 46922*5^37483+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2
46922*5^37483+1 is prime! (155.2515s+0.0060s)

Cheers, Micha

 Templus 2005-02-12 00:02

k=34094

34094*5^27305+1 is prime!!! [19090 digits]

Resevering k=26798 and 27676

 pcco74 2005-02-14 02:15

Hey, 51460*5^50468+1 is prime. (35281 digits)

Primality testing 51460*5^50468+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2
Calling Brillhart-Lehmer-Selfridge with factored part 99.99%
51460*5^50468+1 is prime! (917.7062s+0.0104s)

 ltd 2005-02-19 08:22

Hi,

my next update.

68416*5^44578+1 is prime.

All my ranges are tested to at least n=59000. I will keep them reserved.

Lars

 robert44444uk 2005-02-22 19:30

Moving out

Group

It appears it is time to graduate from "fun stuff" but the thing is how? It seems to me there is a gentlemenly protocol here.

I think we need to be invited to another forum, maybe "prime sierpinski project" but we need to be invited as we would not like people to think we are stealing their valued members and resources. Or we could start a new forum in preparation for the Riesel exercise that Geoff and I are preparing the group for.

And then there is the question of moving all the messages out, rather than just starting again.

If anyone has an idea please post it, or even better move the threads to a nice new home.

Regards

Robert Smith

 geoff 2005-02-23 00:01

If a new forum is created I think it is possible to just move this thread there, I think that is how some other projects started. I volunteer to be a moderator if needed.

results: 86354*5^53329+1 is prime.
releasing: 83936, 84284 (no primes for n <= 100,000).
reserving: 90056, 90676

 robert44444uk 2005-02-23 23:45

Decision time

I think if Geoff can organise to set up a new forum with stickies right left and centre then this is the best solution. We should have at least two threads, Sierpinski and Riesel. Geoff you should send a private message to one of the organisers of the Mersenne site to arrange it.

Here are some results for the 110000-120000 range, apologies for duplications. I give up my reservations in this range.

No primes and highest tested:

110242 52766
110488 55772
110846 31969
111382 55774
111424 53896
111688 51102
113156 62153
117434 64335
118388 50885
118568 139237

One prime:

111502 134008
111994 30446
114158 45859
118450 41654

I reserve candidates in the 140000 to 150000 range.

Regards

Robert Smith

 geoff 2005-02-25 00:39

New Forum

I have created the sticky reservation threads, so the forum is functional now. Please check your existing reservations and let me know if there are any mistakes.

Still needed are posts to explain to newcomers what the project is about, how to get started, etc.. If anyone can help with this then please do, otherwise I will get around to it in the next week.

What do you think is the best way to record the primes found so far? I will keep the text files at [url]http://www.geocities.com/g_w_reynolds/Sierpinski5/[/url] and [url]http://www.geocities.com/g_w_reynolds/Riesel5/[/url] updated for now, but maybe a results thread would be better?

Any other suggestions for the forum, let me know.

 masser 2005-02-26 18:52

129028*5^32462+1 is prime!

 geoff 2005-04-18 03:37

Congratulations masser, this prime made it into the top 5000:
Found the following prime: 76246*5^83568+1
[/quote]

 masser 2005-05-24 15:25

128896*5^89436+1 is prime!

 axn 2005-05-28 07:53

159106*5^89982+1 is prime!!

 ValerieVonck 2005-06-03 18:27

53858*5^33760-1 is prime! 23602 digits

 Footmaster 2005-06-06 08:03

98288*5^42133+1 is Prime!

 Footmaster 2005-06-07 07:29

77908*5^47338+1 is Prime!

 Footmaster 2005-06-07 12:38

78002*5^40115+1 is Prime!

 geoff 2005-06-08 04:17

Please post reservations and results etc. in the reservations thread, it makes it easier for me to keep track of them, and also easier to see what is still available if others make a reservation before I get around to updating the table.

Post a copy of the primes found to this thread if you want, as I will delete the messages in the reservations thread when the tables are updated.

 axn 2005-06-14 05:37

137336*5^47704-1 is prime!

 ValerieVonck 2005-06-14 18:02

53858*5^89840 - 1 is prime! 62801 digits

Woohoo!!!

 ValerieVonck 2005-06-15 09:00

BTW this is a top 5000 prime:

[url]http://primes.utm.edu/primes/page.php?id=74786[/url]

 geoff 2005-06-15 17:27

[QUOTE=CedricVonck]53858*5^89840 - 1 is prime! 62801 digits[/QUOTE]
You found the prime 53858*5^33760-1 earlier, so this k has already been eliminated...

 ValerieVonck 2005-06-15 20:25

[QUOTE=geoff]You found the prime 53858*5^33760-1 earlier, so this k has already been eliminated...[/QUOTE]

?? Is this not a project like "primesearch"??

 geoff 2005-06-17 17:29

[QUOTE=CedricVonck]?? Is this not a project like "primesearch"??[/QUOTE]
Not quite, we are trying to find a prime of the form k*5^n+1 (resp. k*5^n-1) to show that k is not a Sierpinski (resp. Riesel) number. One prime for each k is sufficient. I think it makes sense to record the smallest prime for each k, since this will minimise the time needed to verify the final proofs.

 axn 2005-06-19 06:07

203036*5^22928-1 is prime!
203036*5^27604-1 is prime! (<-- Redundant)

 axn 2005-06-21 07:57

145114*5^31459-1 is prime!

 axn 2005-06-21 09:08

214958*5^20254-1 is prime!

 axn 2005-06-21 11:06

136588*5^22917-1 is prime!

 axn 2005-06-22 03:43

43156*5^44135-1 is prime!

 axn 2005-06-23 03:35

294698*5^47110-1 is prime!

 jaat 2005-07-18 16:55

Another one bites the dust

Prime 9164*5^40892-1

Is there some other way to check these are primes. As the test has some chance of being wrong.(Am i right?)

8494 and 38348 completed upto 50k without any luck.

Btw, Is there some statistics/guesses as to how many will fall till say 50k?
I got 2/4.

jaat

 rogue 2005-07-18 17:54

[QUOTE=jaat]Another one bites the dust

Prime 9164*5^40892-1

Is there some other way to check these are primes. As the test has some chance of being wrong.(Am i right?)[/QUOTE]

Yes, you can use WinPFGW to do a primality test with the -tp switch (or -tm for a +1 number). No, unless there is a bug in the software or if there were a hardware problem, the number is prime.

 geoff 2005-07-19 09:40

[QUOTE=jaat]Btw, Is there some statistics/guesses as to how many will fall till say 50k?
I got 2/4.[/QUOTE]
From the Sierpinski data so far I would guess that a little more than 1 in 3 candidates will be eliminated by finding a prime with an exponent between 20,000 and 50,000. The 4 candidates you worked on were of average combined weight, so I would say you did just a little better than average to eliminate 2.

(I moved the last two messages from the reservations thread)

 jaat 2005-07-19 20:21

Thanks to both Rogue and geoff for answering the queries. I checked both the numbers with the WinPFGW and they are prime. It is also nice to know that one can knock a very large fraction of them very quickly. I'll get back to them soon.

jaat

 geoff 2005-08-14 05:31

I wondered if any of the primes we find could be one of a pair of twin primes of the form k*5^n+/-1.

Since in any three consecutive integers one must be divisible by 3, for both k*5^n+1 and k*5^n-1 to be prime, k must be divisible by 3. It turns out that this is possible for just one of the k we are currently testing, the Riesel candidate k=151026.

Of the primes already found, the two largest twin primes of this form were 110538*5^139+/-1 and 136674*5^172+/-1.

 OmbooHankvald 2005-09-15 07:29

Hey all. I was wondering: Is this project still "alive"? There is not a lot going on in the forum and only geoff has found primes in the last month, so I started to wonder how many people (or GHz) are working on this problem?

I think I'll get back here when I'm finished with my 2721...

 geoff 2005-09-17 15:16

I have a part time 2.66GHz P4 that I split between this project and PSP, it usually does 8-10 hours per week.

It is quiet at the moment, but that is OK, there is no rush :-)

 axn 2005-10-11 07:47

99356*5^34994-1 is prime!

 axn 2005-10-21 04:29

159622*5^21567-1 is prime

86762*5^22292-1 is prime

 axn 2005-10-21 07:33

319658*5^27530-1 is prime!

 axn 2005-10-22 05:25

171064*5^34767-1 is prime!

 axn 2005-10-23 11:37

119456*5^36424-1 is prime!

 axn 2005-10-24 03:48

166186*5^38297-1 is prime!

 jaat 2005-10-28 19:12

45434*5^43736-1 is prime!

 geoff 2005-10-31 10:29

Moderation

From next week I will not have frequent internet access, so if anyone is interested in taking over as moderator then you are welcome. I don't have any scripts for maintaining the project data, I have just done it by hand, but there is not a lot of work, and after the easy primes are found it the amount of work involved will decrease.

A new moderator would need to copy of the files at [url]http://www.geocities.com/g_w_reynolds/Sierpinski5/[/url] and [url]http://www.geocities.com/g_w_reynolds/Riesel5[/url] to somewhere they have write access, and contact Xyzzy for moderator status to be able to edit the reservation threads.

I am going to pack my life into a bicycle trailer and spend the next six months or so on the road or tramping through our national parks. I will log on from internet cafes when I get the chance, but I don't expect to spend a lot of time online.

Keep posting your results, even if nobody picks up the moderation duties I will eventually get back to it. Good luck with the search.

Geoff.

 robert44444uk 2005-10-31 12:35

Geoff

I am so jealous. What I would do with 6 months of the open air life. Sigh!

All the best and stay safe!

Regards

Robert Smith

 axn 2005-11-02 08:41

The following are all primes:
[CODE] 115786*5^20263-1
125458*5^20491-1
184204*5^20027-1
200132*5^20908-1
246046*5^20363-1
253924*5^21023-1
269638*5^21525-1
276142*5^21017-1
299006*5^21356-1
309928*5^20687-1
337856*5^20680-1[/CODE]

 axn 2005-11-02 13:41

152872*5^22021-1 is prime!

 axn 2005-11-03 03:56

258838*5^22831-1 is prime!

 axn 2005-11-03 09:28

67016*5^23070-1 is prime!

 axn 2005-11-04 06:46

66412*5^23375-1 is prime!
132478*5^23391-1 is prime!
138664*5^23489-1 is prime!

 axn 2005-11-04 08:39

244388*5^23898-1 is prime!

 axn 2005-11-05 14:58

86594*5^24026-1 is prime!
87146*5^24448-1 is prime!
91684*5^24459-1 is prime!
272794*5^24845-1 is prime!

 axn 2005-11-07 03:03

99698*5^25322-1 is prime!
150142*5^25325-1 is prime!
121438*5^25453-1 is prime!

 axn 2005-11-07 05:59

259232*5^26132-1 is prime!

 axn 2005-11-08 03:48

338144*5^26554-1 is prime!
309046*5^26573-1 is prime!
208454*5^26620-1 is prime!

 axn 2005-11-08 10:17

119144*5^27036-1 is prime!

 axn 2005-11-09 04:09

271868*5^27312-1 is prime!
66494*5^27496-1 is prime!

PS:- I have got the moderator privileges. But I'll need to figure out how to update the project status files, before I start doing active bookkeeping.

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