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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

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