Octoproths

[Dougy]

Here's two small ones I found using axn1's program.

8299358445 50
3920165865 54

[Dougy]

And of course as soon as I posted those I found some more...

13419352155 52
14002823745 52
19306888875 52
26648959155 52

[axn]

k = 405777203685, n = 120

Thats the only one for k < 10^13.

Robert, the last attachment had a windows executable (console mode). You can run it from cmd prompt and redirect the output to a file.

[axn]

Originally Posted by axn1

One more to the list for n = 97

6832047128535

The rest for n = 97:

8246997577755
8883883726185
9417272582445
9910177359165

These are the last for k < 10^13

[robert44444uk]

Oops should have tried first!

However, how do you write the line script to create an output file? It is years since I saw dos.

I tried this

c:\octo 50 10

and got an output on my screen with about 10 candidates. Are these candidates or are they in fact octos?

Sorry to be a bit naive, but I cannot read music and I cannot read other people's computer programs!

Regards

Robert Smith

[robert44444uk]

I ran Axn1's prgram, up to 10^10 for n=50 through 58. The number of candidates (octos?) produced by the programme are:

50 11
51 5
52 47
53 7
54 28
55 27
56 5
57 18
58 17

I wonder what is so special about 52, it seems statistically well outside of normal variances?

Regards

Robert Smith

This sounds like a nice easy addition to RMA 1.74, and will be listed under "Preferences" "Other options" "Octoproth".
I'll need about a week to get on it.

If there are any additional behaviours or options, that you think should be included under the octoproth option, please post them.


TTn

[axn]

Originally Posted by robert44444uk

However, how do you write the line script to create an output file? It is years since I saw dos.

octo 50 10 > candidates.txt

Originally Posted by robert44444uk

I wonder what is so special about 52, it seems statistically well outside of normal variances?

Yes. I too have observed this. A few posts back, I had said that 81 was "low weight" compared to 82. My guess is that for some of the n's, some small prime(s) might be eliminating a lot of candidates. Conversely, some n's might be escaping these small primes.

Incidentally, these "heavy weight" n's all seem to be of the form 3x+1.

[robert44444uk]

Playing around with Axn1's software has allowed Great Britain to regain the World record for largest octoproth. Hurrah for that, hip, hip, hooray.

374526655755*2^113+1 is 3-PRP! (0.0001s+0.0002s)
374526655755*2^113-1 is 3-PRP! (0.0001s+0.0045s)
- Twin -
374526655755*2^(113+1)+1 is 3-PRP! (0.0001s+0.0079s)
374526655755*2^(113+1)-1 is 3-PRP! (0.0001s+0.0045s)
- BiTwin -
2^113+374526655755 is 3-PRP! (0.0030s+0.0002s)
2^113-374526655755 is 3-PRP! (0.0001s+0.0067s)
2^(113+1)+374526655755 is 3-PRP! (0.0001s+0.0042s)
2^(113+1)-374526655755 is 3-PRP! (0.0001s+0.0042s)
- Complete Set -

Regards

Robert Smith

[Dougy]

Well done robert, they're all prime by the way. However the largest known is
k=405777203685 n=120 found by axn1.

[Dougy]

These are the smallest octoproths for their corresponding bases. Why 56 is so large is a real head-scratcher.

8299358445 50
106546113135 51
13419352155 52
216800357445 53
3920165865 54
72038479785 55
590925115935 56
138429315465 57
84183246225 58
107884757295 59