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257,885,161-1

Edited: 5 Feb 2013, 2:54 p.m. after one or more responses were posted

Actually, that's 2^57885161-1, not 2^257885161-1. The extra "2" makes quite a difference.

Still quite a find!

Whoops! Corrected. Thanks Jim.

Drat! My HP-19C was working on that one last month when it ran out of paper ;-)

I have to out myself as an early SETI@home-member (I think I registered as user 6xx), having run the Mersenne program as well.

But: I think the resources needed for crunching are way too wasteful for the goals reached.


Just consider the standard office PC going from 50W to 100W (no more idle time!), that's 500-1000Wh energy wasted per day, or roundabout 50-100USD of electrical energy - per user, per year. If you work in an AC'ed office, the numbers probably double.

The stats currently mention 100000 active users, and 4 years of crunching time. So we are in the 20 million USD+ range of electrical power used to calculate this number (not even including raised fault rates of the computer parts due to heavier use). One simple word: Ouch.

By their stats, those 100000 users have 730562 computers registered, so the picture is even uglier.

Ouch is right.

Quote:
One simple word: Ouch.

Another simple word: Bollocks.

Regards.

V.

Over 17 million digits - it would take a good number of years just for a human to write all the numbers of this number.

Wow.

It boggles the mind, just like we know of a million digits of pi.

Whenever M_n = 2^n-1 is prime, the larger number P_n = (4^n - 2^n)/2 is "perfect", i.e. its factors add up to the number itself.

n=2: M_n = 3, P_n = 6 = 1 + 2 + 3

n=3: M_n = 7, P_n = 28 = 1 + 2 + 4 + 7 + 14

n=5: M_n = 31, P_n = 496 = 1 + 2 + 4 + 8 + 16 + 31 + 62 +124 + 248

This new Mercenne prime makes for a new perfect number.

At a rough guess, the number of digits in a Mercenne prime is approx 30% of n, and the number of digits in the corresponding perfect number is twice this, approx 60% of n.
(Exercise for the reader: prove this.)

Edited: 16 Feb 2013, 11:08 a.m.

Quote:
prove this

log(an) = n log(a)

log(2) = 0.30103 ~ 30%

Quote:
This new Mercenne prime makes for a new perfect number.



Yes, an even perfect number. Interested readers might like to try and find an odd perfect number and thus make worldwide news.

After all, it's never been proved that there are none, so this is your chance to make math history ... XD

Best regards.


V.