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Old 2003-12-07, 17:19   #23
Evgeny Dolgov
 

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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
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Old 2003-12-07, 17:22   #24
Evgeny Dolgov
 

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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
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Old 2003-12-07, 18:12   #25
smh
 
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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.
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Old 2003-12-07, 18:30   #26
Raptor
 
Dec 2003

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@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.
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Old 2003-12-07, 21:28   #27
flava
 
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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).
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Old 2003-12-08, 08:19   #28
Evgeny Dolgov
 

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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
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Old 2003-12-08, 22:43   #29
ET_
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"Luigi"
Aug 2002
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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
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Old 2003-12-08, 22:45   #30
BMgf
 
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Default 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
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Old 2003-12-08, 22:58   #31
mark hemmeyer
 

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does it help if n is prime?
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Old 2003-12-09, 08:39   #32
BMgf
 
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Dec 2003

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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
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Old 2003-12-09, 16:13   #33
ET_
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"Luigi"
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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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