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Old 2010-07-25, 22:04   #23
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Quote:
Originally Posted by CRGreathouse View Post
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
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Old 2010-07-25, 23:07   #24
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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
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Old 2010-07-26, 00:57   #25
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Quote:
Originally Posted by 3.14159 View Post
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!
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Old 2010-07-26, 01:21   #26
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Code:
100100010001000010001000100100001000001000000001000000000000100000001000000000000100000000000000000000000000001000000100000000000000001
135 digits? Try a 1200-digit prime.

Last fiddled with by 3.14159 on 2010-07-26 at 01:30
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Old 2010-07-26, 01:31   #27
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Quote:
Originally Posted by 3.14159 View Post
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!

What about this one:
Code:
1000100101000001000100001000010010000010001000001010000101000010111111111101111111011101111111111111111001010101000100110111111111111011111110111011111110111010010110010101001010101010111101011101011001
202 digits. Can you beat this?
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Old 2010-07-26, 02:03   #28
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Well, there's always (10^109297 - 1)/9...
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Old 2010-07-26, 02:07   #29
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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
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Old 2010-07-26, 02:10   #30
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Quote:
Originally Posted by CRGreathouse View Post
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'
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Old 2010-07-26, 02:11   #31
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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
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Old 2010-07-26, 02:46   #32
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Quote:
Originally Posted by 3.14159 View Post
Woah, step off the high house, buddy. That record shall be snapped.
No, but now!

Try
Code:
10010010010100100100100100100100100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
500 digits!
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Old 2010-07-26, 07:14   #33
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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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