mersenneforum.org Have Found Principle to generate infinitive PRIME NUMBERS
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 2003-12-07, 17:19 #23 Evgeny Dolgov   22·1,667 Posts Hi! i'm continue using my new method that results i posted yerstaday and have obtained easily next prime numbers count of digits in prime numbers (using my algorithm) (i have tested and all success) (http://www.alpertron.com.ar/ECM.HTM i used this site to test next my prime numbers) # of digits 7 11 15 17 25 35 91 127 203 355 629 647 685 all of these numbers are primes if you want i can send you this numbers like examples So i have found easy method to generate infinitive prime numbers using my very simple rule. All prime numbers i have tested using my notebook in one evening . it is most hard - to input numbers in field of test form i 'll want to use some automatic cases or tool to input more huge numbers i think i'll post results at monday of prime numbers with in 10 000 digits using only my notebook and my simple rule. I know how looks PRIME NUMBER with 10 000 000 digits or more digits today at this moment! but i have only notebook i need more cases or computers to verify primility of generated prime numbers (i fully tested for primility last prime numbers with 685 digits about 4 hours ) but if the number is composite - it takes 2 seconds!!!! i can predict very very huge prime number - with any count of digits (1 000 000 000 and more) now i'm testing properties So any help or advices will be good if you can help with automatic cases that help to input very large numbers http://www.alpertron.com.ar/ECM.HTM - is the best tool that i'm using today Evgeny Dolgov This is previous 647 digit PRIME number you can test it to proof 10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003 tnanks for reply
 2003-12-07, 17:22 #24 Evgeny Dolgov   33·59 Posts corrected post with sample 647 digit prime number you cant test it to proof 100000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000 000000100000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000 0000000000003 Evgeny Dolgov
2003-12-07, 18:12   #25
smh

"Sander"
Oct 2002
52.345322,5.52471

4A516 Posts

Quote:
 (i fully tested for primility last prime numbers with 685 digits about 4 hours ) but if the number is composite - it takes 2 seconds!!!!

This is only for 685 digit numbers

How long do you think it will take to just test a 1 million digit?

And what about a primality test for a number of only a couple of thousand digits?

If you need faster tools, try primo for primality test and winpfgw for prp tests.

 2003-12-07, 18:30 #26 Raptor   Dec 2003 28 Posts @Evgeny Dolgov Even if your prime generator produces hundreds or thousands of primes in a lower digit range (where you can brute-force attack the numbers) this does not prove that the next number the generator ejects is also a prime. What is needed is a _mathematical_ proof, which can only come from the algorithm you use. A number with 10 Million digits is far beyond the range where you can proof its primalty with any known algorithm. Numbers in this range can only be attacked if they have a special form - like 2^p-1 . So again: A proof can only come from your algorithm. So my suggestion to you: just publish your algorithm in the math section of this forum and become famous - or learn.
 2003-12-07, 21:28 #27 flava     Feb 2003 2×59 Posts If you want to test numbers of the form 10^(2*n)+10^n+3, you can use pfgw.exe for probable prime testing. If you use the following input file: ABC2 10^(2*$a)+10^$a+3 a: from 1 to 2000 b: from 0 to 0 you get the following probable primes: 10^(2*1)+10^(1)+3 10^(2*2)+10^(2)+3 10^(2*3)+10^(3)+3 10^(2*5)+10^(5)+3 10^(2*7)+10^(7)+3 10^(2*8)+10^(8)+3 10^(2*12)+10^(12)+3 10^(2*17)+10^(17)+3 10^(2*45)+10^(45)+3 10^(2*63)+10^(63)+3 10^(2*101)+10^(101)+3 10^(2*177)+10^(177)+3 10^(2*314)+10^(314)+3 10^(2*323)+10^(323)+3 10^(2*342)+10^(342)+3 10^(2*367)+10^(367)+3 10^(2*792)+10^(792)+3 10^(2*894)+10^(894)+3 10^(2*1475)+10^(1475)+3 10^(2*1913)+10^(1913)+3 As you can see, the distribution is quite normal and they are more and more distanced. It is very probable that there are in fact very few primes of this forms that have more than a couple of thousend digits. The bad news is the numbers of this form are very hard to proove prime (when they get big).
 2003-12-08, 08:19 #28 Evgeny Dolgov   24×5×41 Posts Hi all! why i'm choosing this form of numbers 10^(n*2)+10^(n)+3 1. simple view 2. symmetric and asymmetric in one time well balanced 3. Predictable step (distribution) 4. Using this tool http://www.alpertron.com.ar/ECM.HTM i have found that if the test number is compiste (not prime) it takes little time to fail this number if the number is fail (not prime) it breaks very fast on parts but if this tool show is unknown and it takes more than 2-3 seconds on numbers with in 685 digits - i know 100% that number is prime!!! and tests show this. (i fully tested) now i'm begining to test numbers with 9555-10000 digits now fail test takes about 1-2 minute - in most hard but in simple - 5 seconds for fail - but if test takes nore than 4-5 (10) minutes with 100% guarantee i say that this number is PRIME (before all this my try was the numbers like 11119 1113 10003 ... - it's wrong numbers they are not productive like that 10....010....03 form or in exponenta 10^(2*n)+10^(n)+3 ) SO MAIN FEATURE - IF TEST NUMBERS in (10....010....03 form or in exponenta 10^(2*n)+10^(n)+3 ) ARE NOT PRIME THEY FAIL VERY FAST!!!!! so the effective search: use test algorithm like in tool http://www.alpertron.com.ar/ECM.HTM and comparing relatively time of success test and time of fail test example if test number - "685 digits" - and test is not failing after 10 seconds the number is PRIME. (100%) (main feature) Evgeny Dolgov You can test this 100000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000 000000100000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000 0000000000003 this numbers is prime - the tool (http://www.alpertron.com.ar/ECM.HTM) is showing "is unknown" - 2 hours and then - is PRIME!!! if you add or remove one digit "0" at the end of this number it fails very fast - not more than 10 seconds on pentium 4 computer. So repeat if test (10^(2*n)+10^(n)+3 form number) using algorithm (http://www.alpertron.com.ar/ECM.HTM) is not failing after relatively short time the number is PRIME. (100%) (main feature) Evgeny Dolgov
2003-12-08, 22:43   #29
ET_
Banned

"Luigi"
Aug 2002
Team Italia

12CE16 Posts

Quote:
 100000000000000000000000000000000000000000000000
The number is certified prime with Primo 2.2.0 beta in 15 minutes on a Athlon XP 2100+

But it's only 685 digits...

Luigi

 2003-12-08, 22:45 #30 BMgf     Dec 2003 24 Posts High level math Let just say that you found some 10 000 000+ digit number for witch you can't find any factor for more than 10 days. What's you next step? Something like GIMPS? Last fiddled with by BMgf on 2003-12-08 at 22:48
 2003-12-08, 22:58 #31 mark hemmeyer   24×7×89 Posts does it help if n is prime?
2003-12-09, 08:39   #32
BMgf

Dec 2003

208 Posts

Quote:
 Originally posted by mark hemmeyer does it help if n is prime?
If 685 digits number is prime then n is even. 10^684 + 10^342 + 3. N=342

2003-12-09, 16:13   #33
ET_
Banned

"Luigi"
Aug 2002
Team Italia

2×29×83 Posts

Quote:
 If 685 digits number is prime then n is even. 10^684 + 10^342 + 3. N=342
Hey, would you mind explaining this one?

Luigi

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