Database for k-b-b's: - Page 17

3.14159 · 2010-09-17, 22:00

(5 * 10²⁵)^{(5 * 10[sup]25})[/sup]??

When it's about 10↑(10↑25) digits?? Woah. Nothing until then. For now, let's consider 5 the smallest value for which this is true.

CRGreathouse · 2010-09-17, 22:28

Quote:

Originally Posted by 3.14159

(5 * 10²⁵)^{(5 * 10[sup]25})[/sup]??

When it's about 10↑(10↑25) digits?? Woah. Nothing until then. For now, let's consider 5 the smallest value for which this is true.

Not that bad -- (5 * 10²⁵)^{5 * 10[sup]25}[/sup] has 'only' about 10²⁷ digits. But it's certainly far beyond the range that could be tested (or even stored!).

3.14159 · 2010-09-17, 22:39

Quote:

Originally Posted by Charles

But it's certainly far beyond the range that could be tested (or even stored!).

If the counterexample is so large that it cannot be tested, let's simply assume 5 is the smallest.

Dougal · 2010-09-17, 22:47

what is the probability that there is a prime below 1,000,000 (for example) digits?

3.14159 · 2010-09-17, 22:49

Quote:

Originally Posted by Dougal

what is the probability that there is a prime below 1,000,000 (for example) digits?

1 in 2302586.

science_man_88 · 2010-09-18, 00:00

Quote:

Originally Posted by 3.14159

1 in 2302586.

that means we'd need to check above on average 10^999993-10^999994

3.14159 · 2010-09-18, 00:08

An example of a prime below 10⁶ digits is 912646 * 798336²⁰¹⁶⁰ + 1 (118995 digits).

3.14159 · 2010-09-18, 00:09

And; to be random; I think someone posted here that there was a 337-digit composite discovered that was pseudoprime to all primes below 200.

Dougal · 2010-09-18, 00:10

what is the probability that there is a prime of the form 5*b^b+1 below 1,000,000 (for example) digits?

3.14159 · 2010-09-18, 00:12

Quote:

Originally Posted by Dougal

what is the probability that there is a prime of the form 5*b^b+1 below 1,000,000 (for example) digits?

See post 176. There should be none smaller than 10²⁷ digits.

Dougal · 2010-09-18, 00:20

Quote:

Originally Posted by 3.14159

See post 176. There should be none smaller than 10²⁷ digits.

no.we'd expect ONE below that,what is the chance,that,that one is below 1,000,000 digits?

2010-09-17, 22:00	#177
3.14159 May 2010 Prime hunting commission. 3220₈ Posts	(5 * 10²⁵)^{(5 * 10[sup]25})[/sup]?? When it's about 10↑(10↑25) digits?? Woah. Nothing until then. For now, let's consider 5 the smallest value for which this is true. Last fiddled with by 3.14159 on 2010-09-17 at 22:06

2010-09-18, 00:08	#183
3.14159 May 2010 Prime hunting commission. 2⁴·3·5·7 Posts	An example of a prime below 10⁶ digits is 912646 * 798336²⁰¹⁶⁰ + 1 (118995 digits). Last fiddled with by 3.14159 on 2010-09-18 at 00:08

2010-09-18, 00:09	#184
3.14159 May 2010 Prime hunting commission. 2⁴·3·5·7 Posts	And; to be random; I think someone posted here that there was a 337-digit composite discovered that was pseudoprime to all primes below 200. Last fiddled with by 3.14159 on 2010-09-18 at 00:10

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2010-09-17, 22:47	#180
Dougal Jan 2009 Ireland 2·3·31 Posts	what is the probability that there is a prime below 1,000,000 (for example) digits?

2010-09-18, 00:10	#185
Dougal Jan 2009 Ireland 2×3×31 Posts	what is the probability that there is a prime of the form 5*b^b+1 below 1,000,000 (for example) digits?