New largest prime number??? - Page 3

cheesehead · 2003-07-12, 17:47

Quote:

Originally Posted by trif

Given that there are many wrong explanations out on the Internet, that might not have done him any good. But he should have at least studied Maxwell's papers on the subject.

howstuffworks.com has the correct explanation.

Assuming the pivot is sufficiently frictionless, if the bulb contains a perfect vacuum, the white (or silvered, in some versions) side will move away from the light source, while the black side approaches it.

If the bulb's vacuum is not perfect, then at some pressure range, the thermal transpiration effect dominates and the black side retreats from the light while the white/silvered side approaches it.

This dual mechanism explains why many folks disagree on the direction of rotation. Two apparently-identical radiometers, side-by-side, could be rotating in opposite directions (I vaguely recall having seen that) because their internal pressures were in different ranges.

See http://science.howstuffworks.com/question239.htm

Regarding thermal transpiration, the results of Maxwell and Reynolds are described at http://math.ucr.edu/home/baez/physics/General/LightMill/light-mill.html

Quote:

I wonder if hydrogen in outer space is of sufficient density to utilize the thermal edge effect that does power Crookes radiometers.

From a solar sailing point-of-view, almost all the Solar System is an excellent vacuum (disregarding little meteoroids which punch negligible holes in the sail) except very close to planets.

Quote:

Might be better to use sails made of of millions of small black discs, if you can keep the heat from becoming too much of a problem.

I suspect that the pressures at which thermal transpiration could be useful occurs only in narrow ranges of planetary atmospheres, where other considerations would effectively prevent its exploitation.

ewmayer · 2003-07-15, 18:15

Quote:

Originally Posted by NickGlover

Someone else should feel free to verify this, but I believe 2^395462042351 - 1 has a 52-bit factor, 4103314151433977.

I seached up to 2^72 and found only the above factor - this took under 10 minutes on a 1GHz Itanium CPU, using a program of my own writing.

ET_ · 2003-07-15, 19:27

what about 2^41234123412341 - 1 ?

:D

Luigi

ewmayer · 2003-07-15, 20:25

Quote:

Originally Posted by ET_

what about 2^41234123412341 - 1 ?

:D

Luigi

No factors < 2^80:

M41234123412341 has 0 factors in [1.000000e+00, 1.208926e+24]
Performed 667856158 trial divides
Clocks = 00:27:13.761
1641.212u 0.002s 27:17.64 100.2% 0+0k 0+0io 116pf+0w

Next thing you'll be telling us it's prime. :)

alienz · 2003-07-15, 21:14

What is the continual beep coming from my computer ever since I finished my last number? The computer has not crashed because every thing is working fine

lycorn · 2003-07-15, 21:38

Quote:

Originally Posted by alienz

What is the continual beep coming from my computer ever since I finished my last number?

:D :D :D :D :D :D 8)

ThomRuley · 2003-07-15, 21:50

Send that to George for verification, you may have a new prime number. Then again, could be a false positive. Only one way to know. :D

ET_ · 2003-07-16, 00:13

Quote:

M41234123412341 has 0 factors in [1.000000e+00, 1.208926e+24]
Performed 667856158 trial divides
Clocks = 00:27:13.761
1641.212u 0.002s 27:17.64 100.2% 0+0k 0+0io 116pf+0w

Next thing you'll be telling us it's prime.

Well, I reached the same limit (1e+24) then the power went off and... :(

Maybe I'll resume the search. But don't stay tuned too much! ;)

Luigi

ewmayer · 2003-07-24, 21:53

Quote:

Originally Posted by ET_

Quote:

M41234123412341 has 0 factors in [1.000000e+00, 1.208926e+24]
Performed 667856158 trial divides
Clocks = 00:27:13.761
1641.212u 0.002s 27:17.64 100.2% 0+0k 0+0io 116pf+0w

Next thing you'll be telling us it's prime.

Well, I reached the same limit (1e+24) then the power went off and... :(

Maybe I'll resume the search. But don't stay tuned too much! ;)

Luigi

I was bored, so I resumed the search, and quickly found this 84-bit factor:

M41234123412341 has a factor: 10437279104937894533506183

-Ernst

antiroach · 2003-07-25, 02:46

ewmayer, how the heck did you go upto 2^72 in only 10 minutes? Maybe you should talk to George and get the algorithm in your trial factoring program into the next version of prime95 :)

NickGlover · 2003-07-25, 04:59

Factoring M395462042351 to 2^72 in 10 minutes is not significantly different from what Prime95 could do. Recall that factoring M395462042351 requires checking 5,000 times fewer factors than M79,300,000. Multiplying 10 minutes * 5,000 yields 34.7 days which is around how long others have said it takes Prime95 to factor M79,300,000 to 2^72.

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2003-07-15, 19:27	#25
ET_ Banned "Luigi" Aug 2002 Team Italia 3·1,619 Posts	what about 2^41234123412341 - 1 ? :D Luigi

2003-07-15, 21:14	#27
alienz Jun 2003 3·7 Posts	What is the continual beep coming from my computer ever since I finished my last number? The computer has not crashed because every thing is working fine

2003-07-15, 21:50	#29
ThomRuley May 2003 443₈ Posts	Send that to George for verification, you may have a new prime number. Then again, could be a false positive. Only one way to know. :D

2003-07-25, 02:46	#32
antiroach Jun 2003 2²·61 Posts	ewmayer, how the heck did you go upto 2^72 in only 10 minutes? Maybe you should talk to George and get the algorithm in your trial factoring program into the next version of prime95 :)

2003-07-25, 04:59	#33
NickGlover Aug 2002 Richland, WA 2²×3×11 Posts	Factoring M395462042351 to 2^72 in 10 minutes is not significantly different from what Prime95 could do. Recall that factoring M395462042351 requires checking 5,000 times fewer factors than M79,300,000. Multiplying 10 minutes * 5,000 yields 34.7 days which is around how long others have said it takes Prime95 to factor M79,300,000 to 2^72.