Archived sieve reservations and discussions - Page 25

wblipp · 2010-09-07, 13:57

Quote:

Originally Posted by mdettweiler

that actually means that after testing exactly 5490 candidates, there is a ~62% chance that a prime will have been found. (Why this is involves some more advanced probability math which I myself don't entirely understand;

If you ran many many tests you would expect to find one per 5490 tests. But in any particular set of tests you might, if you were lucky, find two or three or four or even more. The only way both statements can be true is that there must be some runs of 5490 that find none.

It's pretty basic probability that if the probability of finding none in one test is 5489/5490, then the probability of finding none in 5490 independent tests must be (5489/5490)^5490. Nothing advanced yet, and that is good enough to get your 62% figure.

The advanced part comes from the observation that this is approximately e^(-1), and a few other limit consequences.

William

mdettweiler · 2010-09-07, 15:51

730T-735T complete, 7102 factors: http://www.sendspace.com/file/lnqulo

Reserving 900T-905T.

Lennart · 2010-09-07, 16:03

Reserving 905T-910T. Lennart

gribozavr · 2010-09-08, 00:27

550T-750T for n=485000-495000 finished. Taking 750T-950T.

Lennart · 2010-09-08, 09:11

http://pgllr.mine.nu/privat/local/tps_905T-910T.txt

905T-910T complete

Reserving 920T-925T

Lennart

Oddball · 2010-09-08, 20:22

910T-920T complete, about 11300 factors found:

http://www.sendspace.com/file/x6ly6k

I'll get 925T-930T.

Lennart · 2010-09-08, 22:13

http://pgllr.mine.nu/privat/local/tps_920T-925T.txt

920T-925T Complete

Reserving 930T-940T

Lennart

Oddball · 2010-09-09, 06:37

925T-930T complete, about 5700 factors found:

http://www.sendspace.com/file/k8o6d0

Reserving 940T-950T.

Oddball · 2010-09-11, 04:52

940T-950T done:

http://www.sendspace.com/file/a46j8s

About 11100 factors found.

edit: Just realized that this is the 2500th post in the TPS forum.

Lennart · 2010-09-11, 19:14

http://pgllr.mine.nu/privat/local/tps_930T-940T.txt

930T-940T Complete Lennart

mdettweiler · 2010-09-11, 20:02

900T-905T complete, 5713 factors: http://www.sendspace.com/file/w449t1

Reserving 950T-955T.

2010-09-08, 09:11	#269
Lennart "Lennart" Jun 2007 2⁵×5×7 Posts	http://pgllr.mine.nu/privat/local/tps_905T-910T.txt 905T-910T complete Reserving 920T-925T Lennart Last fiddled with by Lennart on 2010-09-08 at 09:12

2010-09-08, 20:22	#270
Oddball May 2010 499₁₀ Posts	910T-920T complete, about 11300 factors found: http://www.sendspace.com/file/x6ly6k I'll get 925T-930T. Last fiddled with by Oddball on 2010-09-08 at 20:28 Reason: range edit

2010-09-11, 04:52	#273
Oddball May 2010 499 Posts	940T-950T done: http://www.sendspace.com/file/a46j8s About 11100 factors found. edit: Just realized that this is the 2500th post in the TPS forum. Last fiddled with by Oddball on 2010-09-11 at 04:53

2010-09-11, 19:14	#274
Lennart "Lennart" Jun 2007 2⁵×5×7 Posts	http://pgllr.mine.nu/privat/local/tps_930T-940T.txt 930T-940T Complete Lennart Last fiddled with by Lennart on 2010-09-11 at 19:14

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2010-09-07, 15:51	#266
mdettweiler A Sunny Moo Aug 2007 USA (GMT-5) 1100001101001₂ Posts	730T-735T complete, 7102 factors: http://www.sendspace.com/file/lnqulo Reserving 900T-905T.

2010-09-07, 16:03	#267
Lennart "Lennart" Jun 2007 2⁵·5·7 Posts	Reserving 905T-910T. Lennart

2010-09-08, 00:27	#268
gribozavr Mar 2005 Internet; Ukraine, Kiev 11·37 Posts	550T-750T for n=485000-495000 finished. Taking 750T-950T.

2010-09-08, 22:13	#271
Lennart "Lennart" Jun 2007 2⁵×5×7 Posts	http://pgllr.mine.nu/privat/local/tps_920T-925T.txt 920T-925T Complete Reserving 930T-940T Lennart

2010-09-09, 06:37	#272
Oddball May 2010 499 Posts	925T-930T complete, about 5700 factors found: http://www.sendspace.com/file/k8o6d0 Reserving 940T-950T.

2010-09-11, 20:02	#275
mdettweiler A Sunny Moo Aug 2007 USA (GMT-5) 6249₁₀ Posts	900T-905T complete, 5713 factors: http://www.sendspace.com/file/w449t1 Reserving 950T-955T.