20151023, 17:53  #1 
"Rashid Naimi"
Oct 2015
Remote to Here/There
3·643 Posts 
The "one billion minus 999,994,000" digits prime number
Hi,
I am looking for a partner/team to try and find a billion digits prime for the EFF prize. I am certain that it can be done using the formula and the proof that all outputs within a range are guaranteed to be primes that I have developed but have not published yet. The computation does not involve any primality tests since all outputs within the range are primes but some variables will need to be fine tuned to make the output within the range. My email address is overwhelmed so the best way to communicate would be to post to this thread. Thanks in advance for your time and suggestions. 
20151023, 18:30  #2 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2^{3}·7·163 Posts 
Run your algorithm and give us a toy example of a tiny 1milliondigit prime.
No need to finetune the parameters  anything from 1 to 35 million digits will be fine and convincing; it doesn't have to be exactly 1,000,000digits. Such a prime is indeed tiny compared to what you are trying to achieve. 
20151023, 18:42  #3 
"/X\(‘‘)/X\"
Jan 2013
2^{3}×359 Posts 

20151023, 18:43  #4 
"Rashid Naimi"
Oct 2015
Remote to Here/There
789_{16} Posts 
I think that's a fair challenge. I am probably a bit old an impatient to write codes myself which is why I thought I would partner with expert programmers on the field. But I should be able to come up with a relatively large prime using Wolfram Alpha or JavaScript (will take much longer to set up my old computers and libraries).
Anyone know if Wolfram Alpha can be set up to run routines and try list of variables? 
20151023, 19:53  #5 
"Mark"
Apr 2003
Between here and the
13476_{8} Posts 
Also, any number you find needs to be proven prime with other software. pfgw will be able to do a PRP test on anything, but there is no quick way to prove primality on most PRPs.
I suggest that you start smaller, about 1,000 decimal digits. If it is relatively easy to find PRPs of that size and they can be proven prime using Primo if pfgw can't handle them. You will need to show that all numbers of that size that you generate with your code are both PRP and prime before anyone takes you seriously. Last fiddled with by rogue on 20151023 at 19:54 
20151023, 21:34  #6  
Nov 2003
16100_{8} Posts 
Quote:


20151023, 21:41  #7 
"Rashid Naimi"
Oct 2015
Remote to Here/There
3×643 Posts 
Thank you Rogue for introducing me to Primo and PFGW.
Can any of them run any sort of routines off the shelf? Or they only take in integers? Last fiddled with by a1call on 20151023 at 21:42 
20151023, 21:41  #8  
Nov 2008
3·167 Posts 
Quote:


20151023, 22:02  #9 
"Mark"
Apr 2003
Between here and the
2·5^{2}·7·17 Posts 

20151023, 22:19  #10  
Aug 2002
Buenos Aires, Argentina
1333_{10} Posts 
Quote:
So if you think that your algorithm always generate huge primes, you should post the algorithm in order to be analyzed. There are some people in this forum that can check very quickly whether you are losing your time or you have something that hundreds of number theorists have not found in centuries. 

20151023, 22:41  #11 
"Rashid Naimi"
Oct 2015
Remote to Here/There
3·643 Posts 
That thread is too long for my time availability.
Was it based on a proof based on number ranges or was it something else? Are there any similar proofs that fail on large numbers due to element divergence? To make it clear. P_{7}#/22^{n} can be proven to be prime for all results less than 49. No primality testing is required. Of course this will become useless for larger numbers when the two sides fail to diverge. Last fiddled with by a1call on 20151023 at 22:47 
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