Tetraproths

Jens K Andersen · 2006-02-22, 02:31

What is missing in this sequence: 8, 12, 16, ...

Define a tetraproth as 4 primes (k*2^n-1, k*2^n+1, 2^n-k, 2^n+k).

An example with 528 and 501 digits:
n = 1662, k = 928985771563090201572026415

Found with prp testing by PrimeForm which also proved k*2^n+/-1.
Marcel Martin's Primo proved 2^n+/-k.

robert44444uk · 2006-02-28, 19:18

Jens

I don't know why I did not think to investigate these forms originally I think I probably decided that octos were harder to find, certainly we did not have the software of Axn1 or R Gerbicz that we have now. There is certainly a wealth of twin primes out there worth investigating to see if there are some monsters out there. Is there a database of twins out there, other than the top 20?

The problem is that we are spreading ourselves rather thinly at the moment. As far as I can see, I am the only one actively looking at the 8- form, and no one as far as I can work out is active in 12- or 16-, unless they are and are not reporting any progress.

Shame really.

Regards

Robert Smith

jasong · 2006-03-02, 02:47

I am doing ecm for odd perfect search. I've gotten to the point where team spirit and keeping up with the forums is getting kind of boring. While I'll probably still be interested in maxing out my cpu in six months, keeping up on the Internet will probably have lost it's appeal. I'm ready to actually learn something, go my own way.

If anyone is willing to "take me under their wing" in terms of teaching me what to do, I'd love to try this project for a week or three. I have a Linux computer and a Windows XP computer. The Linux computer has a 1.2GHz Athlon with 256K of cache and the XP computer has a 1.75GHz Sempron, also with 256K of cache, although it's defunct at the moment because of a dead power supply. I'm hoping to fix that tomorrow night.

Your help is appreciated.

robert44444uk · 2006-03-02, 08:41

Jasong

Possibly the best use of three weeks of computer time would be the search for the highest Octoproth or possibly Docecaproths - see one of the other threads in this subforum.

I am looking for the largest Octoproth, through looking at a Block of 15 n and using R Gerbicz's software and small batches at each n. Small batches are advised because any batch command line must be completed in full - no breaks are allowed.

Totally virgin territory are tetraproths, however no-one has written any software for this yet.

Anyway, thank you for your interest and we look forwards to you contribution.

Regards

Robert Smith

Jens K Andersen · 2006-03-03, 01:03

Including larger tuplets, there are around 350 titanic twins in the complete Prime Pages database.
This is far too few to expect a tetraproth. I have tested most without success.
There may be larger private twin databases but the tetraproth chance seems too small. Most titanic twins have been found on forms that would give negative 2^n-k.

My sieve could sieve a titanic tetraproth to around 10^11.
The total expectation with PrimeForm/GW prp'ing for 1000 and 1100 digits looks a little below a GHz month. I don't have the cpu time.

robert44444uk · 2006-03-05, 13:31

Group

The smallest tetra at each n is as follows:

n k
1 none
2 1
3 none
4 none
5 none
6 33
7 21
8 57
9 45
10 15
11 741
12 165
13 none
14 993
15 345
16 1833
17 1875
18 765
19 5019
20 447
21 9159
22 6573
23 9591
24 5607
25 12999
26 16017
27 5451
28 29925
29 3675
30 3153
31 12921
32 126483
33 20559
34 71547
35 17871
36 3783
37 36009
38 30387
39 1995
40 32277
41 19929
42 24573
43 62475
44 38415
45 15405
46 13167
47 44925
48 29397
49 191205
50 106497
51 24105
52 435987
53 33111
54 99015
55 447399
56 176463
57 227409
58 225303
59 865725
60 3273
61 10605
62 34377
63 86865
64 582135
65 121611
66 63093
67 85701
68 48783
69 141351
70 21573
71 105729
72 190515
73 194139
74 2760633
75 20991
76 2570007
77 514311
78 82197
79 49041
80 1928115
81 139941
82 391917
83 146511
84 979617
85 2093295
86 1297857
87 22005
88 89403
89 1511601
90 702123
91 2043621
92 687597
93 831051
94 1097445
95 4392891
96 693483
97 555465
98 615987
99 925731
100 1297437

Regards

Robert Smith

2006-02-22, 02:31	#1
Jens K Andersen Feb 2006 Denmark E6₁₆ Posts	Tetraproths What is missing in this sequence: 8, 12, 16, ... Define a tetraproth as 4 primes (k2^n-1, k2^n+1, 2^n-k, 2^n+k). An example with 528 and 501 digits: n = 1662, k = 928985771563090201572026415 Found with prp testing by PrimeForm which also proved k*2^n+/-1. Marcel Martin's Primo proved 2^n+/-k.

2006-02-28, 19:18	#2
robert44444uk Jun 2003 Suva, Fiji 2³×3×5×17 Posts	Tetras Jens I don't know why I did not think to investigate these forms originally I think I probably decided that octos were harder to find, certainly we did not have the software of Axn1 or R Gerbicz that we have now. There is certainly a wealth of twin primes out there worth investigating to see if there are some monsters out there. Is there a database of twins out there, other than the top 20? The problem is that we are spreading ourselves rather thinly at the moment. As far as I can see, I am the only one actively looking at the 8- form, and no one as far as I can work out is active in 12- or 16-, unless they are and are not reporting any progress. Shame really. Regards Robert Smith

2006-03-02, 08:41	#4
robert44444uk Jun 2003 Suva, Fiji 2³·3·5·17 Posts	Best for 3 weeks Jasong Possibly the best use of three weeks of computer time would be the search for the highest Octoproth or possibly Docecaproths - see one of the other threads in this subforum. I am looking for the largest Octoproth, through looking at a Block of 15 n and using R Gerbicz's software and small batches at each n. Small batches are advised because any batch command line must be completed in full - no breaks are allowed. Totally virgin territory are tetraproths, however no-one has written any software for this yet. Anyway, thank you for your interest and we look forwards to you contribution. Regards Robert Smith

2006-03-05, 13:31	#6
robert44444uk Jun 2003 Suva, Fiji 3770₈ Posts	Small tetras Group The smallest tetra at each n is as follows: n k 1 none 2 1 3 none 4 none 5 none 6 33 7 21 8 57 9 45 10 15 11 741 12 165 13 none 14 993 15 345 16 1833 17 1875 18 765 19 5019 20 447 21 9159 22 6573 23 9591 24 5607 25 12999 26 16017 27 5451 28 29925 29 3675 30 3153 31 12921 32 126483 33 20559 34 71547 35 17871 36 3783 37 36009 38 30387 39 1995 40 32277 41 19929 42 24573 43 62475 44 38415 45 15405 46 13167 47 44925 48 29397 49 191205 50 106497 51 24105 52 435987 53 33111 54 99015 55 447399 56 176463 57 227409 58 225303 59 865725 60 3273 61 10605 62 34377 63 86865 64 582135 65 121611 66 63093 67 85701 68 48783 69 141351 70 21573 71 105729 72 190515 73 194139 74 2760633 75 20991 76 2570007 77 514311 78 82197 79 49041 80 1928115 81 139941 82 391917 83 146511 84 979617 85 2093295 86 1297857 87 22005 88 89403 89 1511601 90 702123 91 2043621 92 687597 93 831051 94 1097445 95 4392891 96 693483 97 555465 98 615987 99 925731 100 1297437 Regards Robert Smith

2006-03-02, 02:47	#3
jasong "Jason Goatcher" Mar 2005 3·7·167 Posts	I am doing ecm for odd perfect search. I've gotten to the point where team spirit and keeping up with the forums is getting kind of boring. While I'll probably still be interested in maxing out my cpu in six months, keeping up on the Internet will probably have lost it's appeal. I'm ready to actually learn something, go my own way. If anyone is willing to "take me under their wing" in terms of teaching me what to do, I'd love to try this project for a week or three. I have a Linux computer and a Windows XP computer. The Linux computer has a 1.2GHz Athlon with 256K of cache and the XP computer has a 1.75GHz Sempron, also with 256K of cache, although it's defunct at the moment because of a dead power supply. I'm hoping to fix that tomorrow night. Your help is appreciated.

2006-03-03, 01:03	#5
Jens K Andersen Feb 2006 Denmark 2·5·23 Posts	Including larger tuplets, there are around 350 titanic twins in the complete Prime Pages database. This is far too few to expect a tetraproth. I have tested most without success. There may be larger private twin databases but the tetraproth chance seems too small. Most titanic twins have been found on forms that would give negative 2^n-k. My sieve could sieve a titanic tetraproth to around 10^11. The total expectation with PrimeForm/GW prp'ing for 1000 and 1100 digits looks a little below a GHz month. I don't have the cpu time.