20050412, 03:13  #34 
Aug 2004
Melbourne, Australia
2^{3}×19 Posts 
Here's two small ones I found using axn1's program.
8299358445 50 3920165865 54 
20050412, 03:23  #35 
Aug 2004
Melbourne, Australia
2^{3}·19 Posts 
And of course as soon as I posted those I found some more...
13419352155 52 14002823745 52 19306888875 52 26648959155 52 
20050412, 03:24  #36 
Jun 2003
29·173 Posts 
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. 
20050412, 09:31  #37  
Jun 2003
11631_{8} Posts 
Quote:
8246997577755 8883883726185 9417272582445 9910177359165 These are the last for k < 10^13 

20050412, 14:58  #38 
Jun 2003
Oxford, UK
3^{2}·5·43 Posts 
Oops
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 
20050412, 15:21  #39 
Jun 2003
Oxford, UK
3^{2}·5·43 Posts 
odd statistics
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 
20050412, 18:49  #40 
2^{2}·19·127 Posts 
Octo RMA1.74
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 
20050413, 09:30  #41  
Jun 2003
29·173 Posts 
Quote:
Quote:
Incidentally, these "heavy weight" n's all seem to be of the form 3x+1. 

20050414, 07:18  #42 
Jun 2003
Oxford, UK
3^{2}·5·43 Posts 
New Record!
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 3PRP! (0.0001s+0.0002s) 374526655755*2^1131 is 3PRP! (0.0001s+0.0045s)  Twin  374526655755*2^(113+1)+1 is 3PRP! (0.0001s+0.0079s) 374526655755*2^(113+1)1 is 3PRP! (0.0001s+0.0045s)  BiTwin  2^113+374526655755 is 3PRP! (0.0030s+0.0002s) 2^113374526655755 is 3PRP! (0.0001s+0.0067s) 2^(113+1)+374526655755 is 3PRP! (0.0001s+0.0042s) 2^(113+1)374526655755 is 3PRP! (0.0001s+0.0042s)  Complete Set  Regards Robert Smith 
20050414, 07:36  #43 
Aug 2004
Melbourne, Australia
2^{3}×19 Posts 
Well done robert, they're all prime by the way. However the largest known is
k=405777203685 n=120 found by axn1. 
20050414, 08:14  #44 
Aug 2004
Melbourne, Australia
2^{3}·19 Posts 
Small Octoproths
These are the smallest octoproths for their corresponding bases. Why 56 is so large is a real headscratcher.
8299358445 50 106546113135 51 13419352155 52 216800357445 53 3920165865 54 72038479785 55 590925115935 56 138429315465 57 84183246225 58 107884757295 59 
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