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    1,111st post and fun looking for probable primes where every digit is 1.


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    1,111st post and fun looking for probable primes where every digit is 1.

    Post by stathmk on Thu Sep 18, 2014 12:15 pm

    This is my 1,111st post on http://wolf3d.darkbb.com. 1,111 isn't prime. It's 11x101. If you have a number with a prime number of digits, every digit is 1, and it also happens to be a probable prime, then it's a repunit probable prime.

    Repunit curiosities: http://www.elektrosoft.it/matematica/repunit/curiosity.htm

    - Go to http://www.alpertron.com.ar/ECM.HTM.
    - Set the number of digits in a group to 999.
    - Uncheck Automatic Switch to SIQS
    - Check Verbose mode
    - Check Use Cunningham tables on server
    - Click change

    - Type a completely random number. It's not very likely to be prime.
    - Type (10^1-1)/9. It's 1 and wouldn't normally be called prime.
    - Type (10^2-1)/9. It's 11 and prime.
    - Type (10^19-1)/9. It's 1,111,111,111,111,111,111 and prime.
    - Type (10^23-1)/9. It's 11,111,111,111,111,111,111,111 and prime.
    - Type (10^317-1)/9. It takes a few minutes to prove as prime.
    - Type (10^1031-1)/9. It takes less than an hour to prove as prime.
    - (10^49081-1)/9 is a probable prime.
    - (10^86453-1)/9 is a probable prime.
    - (10^109297-1)/9 is a probable prime.
    - (10^270343-1)/9 is a probable prime.
    - The next repunit probable prime would have more than 3 million digits and would take hours to 3 days to prove as a probable prime with Windows XP or faster.

    I volunteered for the Repunit Project on about 11-11-2011. Iíve now tested over 1,111 repunits. Now that Iíve had a 1,111st post about repunits, I'm going to finish my current testing list, tie up the loose ends of what I'm doing, and quit the project this year. I need to move on and work on http://www.wolfensteingoodies.com and other aspects of my personal life.

    Just for fun, you might want to a test few repunit candidates for the Repunit Project. Go to http://www.elektrosoft.it/matematica/repunit/repunit.htm to contact Maksym Voznyy, Danilo, and Giovanni, they will give you a list of numbers, and tell you how to set up. No previous computer code experience is necessary. Maybe you could test 11 or 12 numbers.† It takes me a little longer than 2 days on 1 of my Windows Vista processors to test one number with over 3 million digits. It's 6 times faster with NVidia Cuda, which I don't have. Contact Danilo about Nvidia Cuda. You can have your computer test it in the background while you sleep, are at work, do homework, check email, or play Windows games because itís a low priority program.

    If you discover a Repunit probable prime, then it will be very near the top at http://www.primenumbers.net/prptop/prptop.php

    This is just for fun.I don't want to obligate anybody to do any of this if they don't want to.

    EDIT: I've asked 3 of the mathematicians and dark_wizzie for permission to post this as my 1,111st post on the forum and nobody objected. I have no plans to post another thread about Mathematics unless we discover the bigger repunit probable prime with over 3 million digits! I joked to dark_wizzie that at the rate that he's posting, he should reach 11,111 posts in the year 2022.

    EDIT 2:† Danilo has contacted me back about the Nvidia Cuda GPU:

    Hi Matt,

    I am fine with your post. Just a small detail you might want to clarify. The GPU program is just for sieving the candidates, it cannot test for primality. Also I would estimate that a GPU is about 100 times faster than sieving on a CPU.

    Hope you are fine.


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