mersenneforum.org Thread for posting tiny primes
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2010-07-25, 22:04   #23
3.14159

May 2010
Prime hunting commission.

24×3×5×7 Posts

Quote:
 Originally Posted by CRGreathouse Yes, I saw the qualification and typed Code: nextprime(10^999)-10^999 into Pari.
Now... How about you settle for larger primes? And, no cheating, they can't be well-known cases.

Next general guideline: 4. Please, whatever you do, do not post their decimal expansion here.

Good luck!

Next: Base: 14; Exponent: 5900; k-range: 56k to 126k.

Also: A so-called "binary prime", a prime which only has digits 1 and 0: 10001010010100101011100010000100001110101101001011101011001011001010100110010101000100110110010010110000001001001 (113 digits)

Can someone find a larger example?

Last fiddled with by 3.14159 on 2010-07-25 at 22:53

 2010-07-25, 23:07 #24 3.14159     May 2010 Prime hunting commission. 168010 Posts Submissions for the range: 67026 * 145900 + 1 (6767 digits) 71412 * 145900 + 1 (6768 digits) 79548 * 145900 + 1 (6768 digits) 83607 * 145900 + 1 (6768 digits) 86286 * 145900 + 1 (6768 digits) 87601 * 145900 + 1 (6768 digits) 102901 * 145900 + 1 (6768 digits) 105651 * 145900 + 1 (6768 digits) 110013 * 145900 + 1 (6768 digits) 118981 * 145900 + 1 (6768 digits) 122151 * 145900 + 1 (6768 digits) Range completed. Last fiddled with by 3.14159 on 2010-07-25 at 23:50
2010-07-26, 00:57   #25
kar_bon

Mar 2006
Germany

3×312 Posts

Quote:
 Originally Posted by 3.14159 Also: A so-called "binary prime", a prime which only has digits 1 and 0: Code: 10001010010100101011100010000100001110101101001011101011001011001010100110010101000100110110010010110000001001001 (113 digits) Can someone find a larger example?
You mean something like this:
Code:
100100010001000010001000100100001000001000000001000000000000100000001000000000000100000000000000000000000000001000000100000000000000001
135 digits!

 2010-07-26, 01:21 #26 3.14159     May 2010 Prime hunting commission. 32208 Posts Code: 100100010001000010001000100100001000001000000001000000000000100000001000000000000100000000000000000000000000001000000100000000000000001 135 digits? Try a 1200-digit prime. Last fiddled with by 3.14159 on 2010-07-26 at 01:30
2010-07-26, 01:31   #27
kar_bon

Mar 2006
Germany

3×312 Posts

Quote:
 Originally Posted by 3.14159 Code: 100100010001000010001000100100001000001000000001000000000000100000001000000000000100000000000000000000000000001000000100000000000000001 135 digits? Try a 1200-digit prime.
Oh, you did it again!

Changed your post! No it's not divisible by a small number (577 you gave if I remember correct).

Which program you used to confirm primeness?

You own PARI-code?

So try another one!

Code:
1000100101000001000100001000010010000010001000001010000101000010111111111101111111011101111111111111111001010101000100110111111111111011111110111011111110111010010110010101001010101010111101011101011001
202 digits. Can you beat this?

 2010-07-26, 02:03 #28 CRGreathouse     Aug 2006 32·5·7·19 Posts Well, there's always (10^109297 - 1)/9...
2010-07-26, 02:07   #29
3.14159

May 2010
Prime hunting commission.

24·3·5·7 Posts

Quote:
 Originally Posted by CRGreathouse Well, there's always (10^109297 - 1)/9...
No well-known cases. Find your *own* primes.

Quote:
 Originally Posted by kar_bon 202 digits. Can you beat this?
Woah, step off the high house, buddy. That record shall be snapped.

Last fiddled with by 3.14159 on 2010-07-26 at 02:11

2010-07-26, 02:10   #30
kar_bon

Mar 2006
Germany

3·312 Posts

Quote:
 Originally Posted by CRGreathouse Well, there's always (10^109297 - 1)/9...
No Rep-Units (I thought of it first, too).
He wanted: 'A so-called "binary prime", a prime which only has digits 1 and 0'

2010-07-26, 02:11   #31
3.14159

May 2010
Prime hunting commission.

24·3·5·7 Posts

Quote:
 Originally Posted by kar_bon No Rep-Units (I thought of it first, too). He wanted: 'A so-called "binary prime", a prime which only has digits 1 and 0'
It also fails the other challenge, because it's a well-known prime.

Last fiddled with by 3.14159 on 2010-07-26 at 02:14

2010-07-26, 02:46   #32
kar_bon

Mar 2006
Germany

3×312 Posts

Quote:
 Originally Posted by 3.14159 Woah, step off the high house, buddy. That record shall be snapped.
No, but now!

Try
Code:
10010010010100100100100100100100100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
500 digits!

 2010-07-26, 07:14 #33 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 223108 Posts Off the top of my head, 11011*10^2212+1 111*10^2230+1 10111*10^2315+1 100111*10^2328+1 110011*10^2426+1 1101*10^2822+1 100101*10^2910+1 are prime. 2910+ digits. But that's peanuts.

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