[QUOTE=Unregistered;346255]... unless the number is confirmed to be "30402461" just 4 off from the original number ...[/QUOTE]

30402461 = 61 * 498401

One of the first things you should know about Mersenne primes is that for 2^n-1 to be prime, n must be prime. There's been no mistake: 2^30402457-1 is a prime number.

These pages have some info about Mersenne numbers/primes:

[URL]http://primes.utm.edu/mersenne/[/URL]
[URL]http://en.wikipedia.org/wiki/Mersenne_prime[/URL]

Still, why 43rd number is an exception?at least to this point from all the Mersenne Numbers that we know of. Not trying to make people angry at me but just out of curiosity.

:crank:

[QUOTE=Unregistered;346275]Still, why 43rd number is an exception?at least to this point from all the Mersenne Numbers that we know of. Not trying to make people angry at me but just out of curiosity.[/QUOTE]

25 is not prime, put it is a prime power. Can you make your theory fit that?

[QUOTE=Mini-Geek;346272]One of the first things you should know about Mersenne primes is that for 2^n-1 to be prime, n must be prime.[/QUOTE]
Furthermore, n will be divisible by 3 if the sum of the digits is a multiple of 3.
Now how many times would you expect the sum of the digits to be 25, 35,49 or 55?
Is it unlikely that we happen to have found only one instance?

[QUOTE=Unregistered;346241]Okay I admit I'm wrong, why this nervousness? Anyway just look up at the image and see whether it is a strange coincidence. Because as you see in D and E column, the numbers are ALWAYS Even or PRIME, with the exception of 43rd number which equals to 25 which is neither even nor prime. Out of 48 numbers this is the only case right know so to make Mersenne numbers even more challenging my question to you and myself aswell is : Is 43rd Mersenne number is the only prime number that his sum is "pure odd without primes", because 1/3 of all numbers can be thrown out and searching for Mersenne numbers can be faciliated.

With Regards,

M.


PS. here is the link: [url]http://tinypic.com/view.php?pic=10e1n42&s=5[/url][/QUOTE]

As I said. Clueless.

Noone is nervous. We just get tired of people who know nothing
about mathematics who come here babbling mindless numerology while
claiming "analysis". We get too many of them.

Half of the sums are expected to be even. The average digit value is
slightly less than 4.5 (The first digit is not uniformly distributed; Benford's
Rule makes it likely to be small). The largest number has 8 digits, so
for the largest number we expect the sum to be about 36.
We expect few numbers to have a sum that is significantly larger than the
expected mean (by the Central Limit Theorem)

The exponent is always prime. so it is no surprise that the sum of digits for 2,3,5,7 The single digit Mersenne exponents) are prime.

Now ask: How many of the odd numbers less than 36 are
NOT divisible by 3? These numbers are 31, 29, 25, 19, 17, 13, 11, 7, and 5.

Bingo!!! Only 25 is composite! And the smaller Mersenne exponents
will have even smaller sums. Ask yourself which of the known Mersenne
prime exponents are big enough to have a digit sum greater than 25???
(especially when taking into account Benford's Rule!) For the smaller
exponents the sum MUST be prime because all of the other odd numbers
are divisible by 3.

[QUOTE=R.D. Silverman;346295]For the smaller
exponents the sum MUST be prime because all of the other odd numbers
are divisible by 3.[/QUOTE]
Shoddy work Silverman.
The sum is often even and not divisible by 3.

[QUOTE=Unregistered;346255]Out of 48 numbers, 27 is prime numbers, ending with 41 which is prime as well. In general sense I don't want to make an argument or something but just curious if this could potentially reduce the numbers you guys as GIMPS teamwork do in order to check which numbers are mersenne numbers withing such big span of numbers. From 1 to 100 we have 74 numbers that are Even + Prime, and the rest 26 are pure odd which is rougly 25% that can be thrown out if we can confirm that only totals that are equal to even or prime number are the Mersenne numbers.

M.[/QUOTE]

Out of the matter of our universe, if you take away the 4% of known matter, the relationship between dark energy and dark matter is 74% - 26%

Does that mean that dark matter/dark energy are tightly linked to prime numbers? I'm afraid not... :smile:

Luigi

[QUOTE=davieddy;346297]Shoddy work Silverman.
The sum is often even and not divisible by 3.[/QUOTE]But give him high marks for effort. Hardly anyone, myself included, would have taken that much trouble to try to educate someone who is presently clueless but may yet be cured of that condition.

"The exponent is always prime. so it is no surprise that the sum of digits for 2,3,5,7 The single digit Mersenne exponents) are prime. "

I didn't asked about single digits as it is logical that sum will be prime....I'm talking about giving a "mathematical prove" or so " Theorem" as you like to call them to prove or disprove why the 43rd Mersenne numbers prime is adding up to 25. Because Yes, I understand that 25 is the only one mentioned while having 8 digits, yet you still didn't answered my question WHY it is 25. and not 23 for instance if all previous numbers hold that it's even or prime. If so it your theorem, what do you predict will happen as it approaches 9.10...11 and so on digits. You suggest that it is to no suprise that the Mersenne number will add to an even or prime yet we see that they don't have to. My idea here is to easy the task as why go through all the combinations if we can throw out Mersenne prime numbers that for sure are not one of them.

With Regards,

M


PS.I'm not trying to inforce my numerological theory yet working witch such numbers as 2^48th Mersenne numbers is for sure not an easy task, and maybe there is an easier approach to it.

[QUOTE=Unregistered;346275]Still, why 43rd number is an exception?at least to this point from all the Mersenne Numbers that we know of.[/QUOTE]Perhaps what Mini-Geek and R.D.Silverman are basically saying is that when one takes into account that all of the decimal-digit sums so far are relatively small (41 or less), there's a high probability that each is either even or prime.

Consider the 40 numbers from 2 to 41. (1 isn't eligible because 2[sup]1[/sup]-1 isn't considered prime.) Half of them are even. That leaves only 20 odd possibilities.

Mersenne primes must have a prime exponent. Any exponent whose digit-sum is a multiple of 3 must be composite (except for 3 itself). So, from the remaining 20 odd numbers, that knocks out 9, 15, 21, 27, 33 and 39.

Left as the only fourteen odd possibilities are: 3, 5, 7, 11, 13, 17, 19, 23, 25, 29, 31, 35, 37 and 41. They're all prime except 25 and 35.

So, there are only two non-even, non-prime numbers less than 42 that can be digit-sums of Mersenne prime exponents ... and, as you've seen, we already have one of them occurring among the 49 exponents known so far.

I expect that, probabilistically, it's not very strange that in 49 "tries" of the 34 possible digit-sums less than 42, we've (a) not seen the particular case of 35 yet, and (b) have seen the particular case of 25.

My combinatorial skill is rusty, so I'll let someone else compute the probabilities in 49 tries of (a) having missed "35", and (b) seeing "25", taking into account that the smallest exponents could not have digit-sums as large as 25 or 35. (Note that we have seen the smaller of those two.)