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
141D_{16} 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
141D_{16} Posts 
Quote:
8246997577755 8883883726185 9417272582445 9910177359165 These are the last for k < 10^13 

20050412, 14:58  #38 
Jun 2003
Oxford, UK
19·103 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
7A5_{16} 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 
3×5×7×19 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
19×271 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
19·103 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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