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New Largest Prime Found: Over 7 Million Digits
Gilchrist continues "If you want to see the number in written in decimal, Perfectly Scientific, Dr. Crandall's company which developed the FFT algorithm used by GIMPS, makes a poster you can order containing the entire number. It is kind of pricey because accurately printing an over-sized poster in 1-point font is not easy! Makes a cool present for the serious math nut in your family.
For more information, the press release is available.
Congratulations to Josh and every GIMPS contributor for their part in this remarkable find. You can download the client for your chance at finding the next world record prime! A forum for newcomers is available to answer any questions you may have.
GIMPS is closing in on the $100,000 Electronic Frontier Foundation award for the first 10-million-digit prime. The new prime is 72% of the size needed, however an award-winning prime could be mere weeks or as much as few years away - that's the fun of math discoveries, said GIMPS founder George Woltman. The GIMPS participant who discovers the prime will receive $50,000. Charity will get $25,000. The rest will be used primarily to fund more prime discoveries. In May 2000, a previous participant won the foundation's $50,000 award for discovering the first million-digit prime."
But Pseudoprimes? Probability of primeness? Hah! You people cut corners!
/^[A-Z0-9._%+-]+@[A-Z0-9.-]+\.[A-Z]{2,4}$/i
... but why exactly is this so important? Can we use this number in any way, or is it just another prime?
Quid festinatio swallonis est aetherfuga inonusti?
Africus aut Europaeus?
The GIMPS Project found this prime. You too can contribute by downloading the client (for various OSes).
Thought I would drive the point home as this is a great DC project that doesn't receive half the attention of some of the more dubious DC projects...
----
I'm still searching for that even prime number bigger than 2...
I'm the Devil the Windows users warned you about.
Say all you will, but Optimus is still the ultimate prime.
I also reply below your current threshold.
Great. This should improve the distribution of elements in my hashtable implementation.
He's also found the largest known perfect number, 2^(24,036,583-1)*((2^24,036,583)-1)
Who knows, one day you might find yourself struck in the tiger den with multiple doors all marked with Mersenne Primes, and a sign saying, "safe exit thru the door marked with the 41st Mersenne Prime". Yeah, then who is gonna bitch about not memorizing that sucker, huh?
Size does matter :)
I heard a rumor that some wiseguy in charge of printing changed one of the digits first - you may think you're paying for a prime, but they're really stiffing you and shipping a composite number!
In binary: 11111111111111111111111111111111111111111111111111 11111111111111111111111111111111111111111111111111 11111111111111111111111111111111111111...
:/
Your comment violated the "postercomment" compression filter. Try less whitespace and/or less repetition. Comment aborted.
Sorry
I have discovered a truly marvelous demonstration of a 10 million digit prime which this margin is too narrow to contain.
i'll let everyone know when i am done!
-- ladies and gentlemen we are floating in space!
Actually the last 9 digits are 733969407, as this simple C program will show you:
// minus 1
#include <stdio.h>
int main()
{
int i;
int p = 1;
int m = 1000000000;
for (i = 0; i < 24036583; i++)
p = p*2 % m;
p = (p+m-1) % m;
printf("%d\n", p);
}
Primality tests for numbers of the form k*b^n+/-1 have always (since Proth's time) been poly time, in fact O(n^(2+eps)).
http://primepages.org/
'proving'
YAW.
Your head of state is a corrupt weasel, I hope you're happy.
Been running prime 95 for 6 years now.
.. ive found no primes but the work ive done would have taken 307 years for a p90 computer to match... a p90 being the 'zero-point' computer when the project started.
Started with a p120 laptop, at times had a dozen computers teamed up.
In that time
George Bush + Linux = "I will not let information get in the way of the fight against Windows"
Theorem For any positive odd integer n, 3 divides 2^n+1
Proof We will use the Principal of Mathematical Induction.
Basis When n=1, we have 2^n+1=2^1+1=3. Furthermore, when n=3, we have 2^n+1=2^3+1=9.
Induction Now suppose n is a positive odd integer, and that 3 divides 2^n+1. We will now show that 3 divides 2^(n+2)+1.
Since 3 divides 2^n+1, there exists an integer q such that 2^n+1=3*q
2^(n+2)+1=2^(n+2)+4-3
=2^2*2^n+4-3
=4*(2^n+1)-3
=4*3*q-3
=3*(4*q-1)
=3*r, r=4*q-1
Where r is an integer by the closure properties of multiplication and subtraction.
QED
More directly (without induction):
if T = 2^(2p+1) + 1:
T = 2^(2p+1) - 2 [mod 3]
T = 2(2^2p - 1) [3]
T = 2(4^p - 1) [3]
T = 2(1^p - 1) [3]
T = 0 [3]
qed
2^(odd number)+1
= (-1)^(odd number)+1 [mod 3]
= -1 + 1 [mod 3]
= 0 [mod 3]