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Old 2006-02-22, 02:31   #1
Jens K Andersen
 
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Feb 2006
Denmark

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Default Tetraproths

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.
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Old 2006-02-28, 19:18   #2
robert44444uk
 
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Jun 2003
Oxford, UK

7BB16 Posts
Default 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
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Old 2006-03-02, 02:47   #3
jasong
 
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"Jason Goatcher"
Mar 2005

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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.
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Old 2006-03-02, 08:41   #4
robert44444uk
 
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Jun 2003
Oxford, UK

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Default 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
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Old 2006-03-03, 01:03   #5
Jens K Andersen
 
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Feb 2006
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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.
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Old 2006-03-05, 13:31   #6
robert44444uk
 
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Jun 2003
Oxford, UK

111101110112 Posts
Default 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
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