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 2003-12-08, 08:33 #1 Evgeny Dolgov   699010 Posts Effective way to generate prime numbers (infinitive) 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 number 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 Last fiddled with by Evgeny Dolgov on 2003-12-08 at 08:35
 2003-12-08, 09:25 #2 TauCeti     Mar 2003 Braunschweig, Germany 3428 Posts You algorithm produces numbers of a special form. Some of them are prime and look interesting in their decimal expansion. By the way: There are a lot of numbers, that look 'interesting' and are prime. Take for example the number 10000...(repeat the '0' for 39017 times)...00001. It is prime. More examples at Prime curious The problem with your algorithm is, that not every number it produces is prime. So you have to check with a 'prime-checker', if it is prime or not. For random numbers of the lenght of 10 million decimals, there is no known algorithm that decides this question in a practicable timeframe. Only for very special prime-candidates (Mersenne Numbers and Generalized Fermat Numbers ) the primality for 10 million decimal numbers can be checked with a computer in some weeks or months. To summarize: As long, as you can not prove mathematically that your algorithm produces a specific prime number of at least 10 million decimals, you have to check the candidates for primality. And that is not possible today for random - or as far as i can see it your - numbers in the 10 million decimals range with known algorithms. Last fiddled with by TauCeti on 2003-12-08 at 09:27

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