when will the 10M Digit prime be found?

Deamiter · 2002-10-21, 06:15

Yeah... so I was bored. Personally, though, I think it'll be sometime in December when my test finishes... :D

hyh1048576 · 2003-08-25, 08:41

I reply it so it can get to the top of the forum :) ......And it's time to discuss it again :D

alienz · 2003-08-25, 13:01

Should we not forget the small ones and go straight for primes M10million. That is where the money is. By the time we get there Piv 4ghz machines will be the norm.

nomadicus · 2003-08-25, 14:17

My belief is that we will discover M40 and M41 before the 10 million prime (assuming that M39 remains as is). Of course that's the current reading into my crystal ball. Hmmm.... I better get some cleaner out and polish that thing just in case.

cheesehead · 2003-08-25, 14:20

Anyone care to prove that there is a ten-million-digit prime to be found?

That is, present a proof that not all integers with exactly 10,000,000 decimal digits (i.e., N such that N is in Z and 10^9,999,999 < N < 10^10,000,000) are composite. Who can present the most elegant proof?

Proof by (counter-)example will be considered the most elegant method. :)

Orgasmic Troll · 2003-08-25, 17:34

let n = 10^9,999,999

there exists a prime p such that n < p < 2n (chebychev's theorem)

2 * 10^9,999,999 has 10 million digits

cheesehead · 2003-08-25, 19:57

That's the one I had in mind, though I didn't recall the theorem's being named after Chebychev. By the same method, for every k > 0 there are at least three primes with k decimal digits.

Is there another elegant proof?

ewmayer · 2003-08-25, 21:04

A related question (albeit one of a probabilistic nature): what is the expected number of primes having exactly 10,000,000 decimal digits?

apocalypse · 2003-08-25, 22:59

Well, if we can assume (without proof :) ) that E[pi(n)], the expected number of primes less than n, is n / ln(n), then the short answer is:

E[pi(n)] = 10^(10^7)/ln(10^(10^7)) - 10^(10^7 - 1)/ln(10^(10^7 - 1))

or, more coarsely, about 3.9 * 10^(10^7 - 8 )

Unelss my math is wrong, in which case it will no doubt be corrected by another poster.

E_tron · 2003-08-26, 02:54

I'm thinking the first 10million digit mersenne prime is above M45

. I just kind of did a curve of the past primes and there location on a number line :D .

According to my little unproved theory, the next mersenne prime is around M25 :D .

Uncwilly · 2003-08-26, 13:07

Shouldn't that be 25Mnot M25? M25 Has been already found.

View Poll Results: When will the first 10 million digit prime number be found?
0, I am not currently running gimps, there is no client for my PDA.	3	3.30%
1, I believe GIMPS is a good use of my time, but am not so in to it as a hobby.	24	26.37%
2-3, I have a small home network, or have my home and work machine on gimps.	25	27.47%
4-6, I have a small network at home/a few machines at work I admin.	24	26.37%
7-15, It is an obcession, true, but one I dreadfully enjoy. This is my mark on history.	15	16.48%
Voters: 91. You may not vote on this poll

2002-10-21, 06:15	#1
Deamiter Sep 2002 3²·13 Posts	when will the 10M Digit prime be found? Yeah... so I was bored. Personally, though, I think it'll be sometime in December when my test finishes... :D

Similar Threads
Thread	Thread Starter	Forum	Replies	Last Post
Smallest prime with a digit sum of 911	Stargate38	Puzzles	6	2014-09-29 14:18
Wowww!!! Exactly 4 digit prime!!!	Merfighters	Lounge	39	2013-04-12 20:26
44-digit factor found using ECM w/ B1=1e6 & B2=1e8	WVU Mersenneer	Factoring	8	2010-04-24 17:01
160 digit factor found of 366 digit (PRP-1)	AntonVrba	Factoring	7	2005-12-06 22:02
10 digit prime in e	TTn	15k Search	15	2004-10-18 03:11

2003-08-25, 08:41	#2
hyh1048576 Jun 2003 2⁶ Posts	I reply it so it can get to the top of the forum :) ......And it's time to discuss it again :D

2003-08-25, 13:01	#3
alienz Jun 2003 3·7 Posts	Should we not forget the small ones and go straight for primes M10million. That is where the money is. By the time we get there Piv 4ghz machines will be the norm.

2003-08-25, 14:17	#4
nomadicus Jan 2003 North Carolina 11110110₂ Posts	My belief is that we will discover M40 and M41 before the 10 million prime (assuming that M39 remains as is). Of course that's the current reading into my crystal ball. Hmmm.... I better get some cleaner out and polish that thing just in case.

2003-08-25, 14:20	#5
cheesehead "Richard B. Woods" Aug 2002 Wisconsin USA 2²×3×641 Posts	Anyone care to prove that there is a ten-million-digit prime to be found? That is, present a proof that not all integers with exactly 10,000,000 decimal digits (i.e., N such that N is in Z and 10^9,999,999 < N < 10^10,000,000) are composite. Who can present the most elegant proof? Proof by (counter-)example will be considered the most elegant method. :)

2003-08-25, 17:34	#6
Orgasmic Troll Cranksta Rap Ayatollah Jul 2003 641 Posts	let n = 10^9,999,999 there exists a prime p such that n < p < 2n (chebychev's theorem) 2 * 10^9,999,999 has 10 million digits

2003-08-25, 19:57	#7
cheesehead "Richard B. Woods" Aug 2002 Wisconsin USA 2²·3·641 Posts	That's the one I had in mind, though I didn't recall the theorem's being named after Chebychev. By the same method, for every k > 0 there are at least three primes with k decimal digits. Is there another elegant proof?

2003-08-25, 21:04	#8
ewmayer ∂²ω=0 Sep 2002 República de California 19×613 Posts	A related question (albeit one of a probabilistic nature): what is the expected number of primes having exactly 10,000,000 decimal digits?

2003-08-25, 22:59	#9
apocalypse Feb 2003 2·3·29 Posts	Well, if we can assume (without proof :) ) that E[pi(n)], the expected number of primes less than n, is n / ln(n), then the short answer is: E[pi(n)] = 10^(10^7)/ln(10^(10^7)) - 10^(10^7 - 1)/ln(10^(10^7 - 1)) or, more coarsely, about 3.9 * 10^(10^7 - 8 ) Unelss my math is wrong, in which case it will no doubt be corrected by another poster.

2003-08-26, 02:54	#10
E_tron Sep 2002 Austin, TX 3·11·17 Posts	I'm thinking the first 10million digit mersenne prime is above M45 . I just kind of did a curve of the past primes and there location on a number line :D . According to my little unproved theory, the next mersenne prime is around M25 :D .

2003-08-26, 13:07	#11
Uncwilly 6809 > 6502 """"""""""""""""""" Aug 2003 101×103 Posts 2×4,909 Posts	Shouldn't that be 25Mnot M25? M25 Has been already found.