Riesel base 6 - team drive #4 - EIGHT OR BUST! - Page 33

Batalov · 2013-01-25, 02:55

Quote:

Originally Posted by gd_barnes

Edit: Here's an interesting side project: Find the smallest 1,000,000-digit base 10 PRIME; that is it must be proven prime. That would be tough...a lot of algebra to come up with a form that factors to 33% that is barely bigger than 10^999999.

One obvious route would be to test numbers of form
2*k*(3139*2^3321905-1)+-1
k should be around a few hundred, because 3139*2^3321905-1 has 999,997 digits. But of course, one will only get lucky after trying a few million k values, so it will be a bit overshot.

gd_barnes · 2013-01-25, 03:34

Quote:

Originally Posted by Batalov

One obvious route would be to test numbers of form
2*k*(3139*2^3321905-1)+-1
k should be around a few hundred, because 3139*2^3321905-1 has 999,997 digits. But of course, one will only get lucky after trying a few million k values, so it will be a bit overshot.

Perhaps the best approach would be to do a fixed-n search and vary k for the simpler forms k*2^3321925-1 and k*2^3321925+1. Once again, you'd overshoot by a few digits before finding a prime but I can't think of a faster approach. To keep getting closer and closer, you could keep lowering the n-values by 1 and start from a slightly higher k-value, i.e. k*2^3321924-1 and k*2^3321924+1 where k>2 or k*2^3321923-1 and k*2^3321923+1 where k>4. This would give you more possible tests at the exact 1,000,000 digit level.

Batalov · 2013-01-25, 07:03

And yet faster approach is to vary 2<=b<=2^20, 1<=k<=K, n~=log₁₀b*999999-X in very narrow K limits (a few thousand, perhaps), with X a few digits below mega₁₀digit limit. Child's play.

gd_barnes · 2013-01-25, 07:20

Quote:

Originally Posted by Batalov

And yet faster approach is to vary 2<=b<=2^20, 1<=k<=K, n~=log₁₀b*999999-X in very narrow K limits (a few thousand, perhaps), with X a few digits below mega₁₀digit limit. Child's play.

Maybe it's child's play for you. :-)

BTW, is 10^999999+736939 the smallest 1,000,000-digit base 10 PRP that was found?

Batalov · 2013-01-25, 07:25

of course not. That's a composite! ;-)

______________
1791777*2^3321904+1 is composite: RES64: [3EF30AB81F9A16F4] (16743.0616s+0.0004s)

Damn! A composite, too! (one of the smallest survivors in k*2^3321900+1 just-for-fun sieve).

One down, a few million more to go. ;-)

LaurV · 2013-01-25, 07:55

And who says that a composite can't be PRP base 10?

gd_barnes · 2013-01-25, 08:06

Quote:

Originally Posted by Batalov

of course not. That's a composite! ;-)

Well...a quick sieve found no factors < 10G for 10^999999+736939 so it would have been very lucky for you to pull that number out of
your head unless you pulled it out of the sieve file from the effort, which I do not have available to me.

Edit: It looks like you would have had < 5% chance of pulling a random odd c-value for the form 10^999999+c and having it survive a sieve to 10G. :-)

Dubslow · 2013-01-25, 08:18

Quote:

Originally Posted by gd_barnes

"Mega" doesn't even necessarily mean million in some contexts. It means 2^20 or 1048576...and it's not a prime search; it's a PRP search...and it's base 10, which isn't clear either (it could have been base 2).

[pedantism]
Well... mega really does mean 10^6, being an SI prefix. Its use in the computer world to mean 2^20 is a side effect of the unfortunate (from this point of view) fact that 2^(x*10) ~ 10^(x*3), or equivalently that log₂10 ~ 3 (that is, approximately an integer). According to the International Electrotechnical Commission, the preferred prefix for 2^20 is mebi.

I completely agree on the PRP/prime thing; as for the base thing, in my book "digit" is pretty pretty unambiguously base ten. "bit" or "binary digit" would mean base 2; thus it would be best termed a megadigit PRP search (megaPRP is still rather ambiguous). Also note that originally the thread did refer to actual primes, but devolved to PRP only since that's the only practical thing at the moment.

[/pedantism]

Man, that homework must have really gotten to me

Puzzle-Peter · 2013-03-18, 15:17

R6 tested n=1300k to 1400k, no prime.

Puzzle-Peter · 2014-01-09, 20:44

Not very much going on here, so I'll take n=1400k to n=1500k.

Puzzle-Peter · 2014-02-25, 22:08

Quote:

Originally Posted by Puzzle-Peter

Not very much going on here, so I'll take n=1400k to n=1500k.

Range finished, results emailed.

2013-01-25, 07:25	#357
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 2⁴·593 Posts	of course not. That's a composite! ;-) ______________ 17917772^3321904+1 is composite: RES64: [3EF30AB81F9A16F4] (16743.0616s+0.0004s) Damn! A composite, too! (one of the smallest survivors in k2^3321900+1 just-for-fun sieve). One down, a few million more to go. ;-) Last fiddled with by Batalov on 2013-01-25 at 23:40

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2013-01-25, 07:03	#355
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 22420₈ Posts	And yet faster approach is to vary 2<=b<=2^20, 1<=k<=K, n~=log₁₀b*999999-X in very narrow K limits (a few thousand, perhaps), with X a few digits below mega₁₀digit limit. Child's play.

2013-01-25, 07:55	#358
LaurV Romulan Interpreter Jun 2011 Thailand 23×419 Posts	And who says that a composite can't be PRP base 10?

2014-01-09, 20:44	#362
Puzzle-Peter Jun 2009 2²·3²·19 Posts	Not very much going on here, so I'll take n=1400k to n=1500k.