ITT: We find a prime larger than the one in my picture.
Does anyone have any good ideas? Anyone have a guess?
you dumb faggot. no one here has a computer that can do this type of shit.
>>8075368
2^(74207281)+1
because 2^(74207281)-1 is the smaller one of a twin prime.
proof that 2^(74207281)-1 is the smaller one of a twin prime is left as an exercise.
Mersenne primes are shit.
>>8075503
that's not technically true
>>8075511
>proof that 2^(74207281)-1 is the smaller one of a twin prime is left as an exercise.
2^(74207281)+1 is either a prime or not.
if it is prime, stop here
if it is not prime, just add plus one and carry on.
>>8075546
Someone who remembers basic number theory get to checking if this number is prime!!!
Someone else assume it isn't, add a few more numbers to it for good measure and check those!
what is the fucking point of this prime number shit seriously. Don't say security or whatever it's fucking pointless can't believe Terence Tao wastes his talent on this shit.
That's a multiple of 3
>>8075623
https://en.wikipedia.org/wiki/Prime_number#Applications
>>8075546
>if it is not prime, just add plus one and carry on.
>just add plus one
>>>>
"the least prime number larger than 2^74207281 - 1"
well-defined by the well-ordering principle and the infinitude of primes
>>8075368
I'll give it a shot:
[math] 2^{74207281} + 3 [/math] may be prime.
>>8075960
Maybes are meaningless.
>>8075635
>he doesn't know how to add plus one
Nobody tell him.
Can someone please use the prime number theorem to find what the actual likely prime number larger than that is?
Like what's the likely distance between prime numbers at this scale?
>>8075960
Thank you for trying.
Is there something inherit to powers of two that make them closer to prime numbers on average or is it just that you can only find large prime number using base 2 computer systems?
>>8076118
Read: https://en.wikipedia.org/wiki/Mersenne_prime
>>8075629
So, in other words, it's mostly to study math.
>>8075511
How do you know it's a twin prime?
>>8076103
>Like what's the likely distance between prime numbers at this scale?
that is a very good question
>>8075368
Didn't it take months to find this though, with lots of computing power.
Someone use this: https://en.wikipedia.org/wiki/Prime_number_theorem
the prime number theorem, to find the likely distance between primes at this level.
>>8076144
Using the prime number theorem and only the list of prime numbers less than this number (there aren't that many), we can make a good estimate and check it pretty easily.
>>8076137
>that is a very good question
OK.
>>8075573
>I have a pen and paper and I understand inverse multiplication.
It's a bit more complicated than that anon. Well, actually not complicated, but basically impossible for humans to do at this point based on how much time it would take. For instance, prove that OPs number is prime, and come back in 7 years once you're done.
>>8076170
But there's actually not very many prime numbers prior to the one in the OP. If I just check all the reasonable combinations of those primes, of which there are very few, I could show that no combination of them equals the prime in question..?
>>8076178
So why wouldn't this: >>8076150
work as a solution?
Rather than factoring by means of sieves, we can check for primality fairly quickly.
>>8076170
There are theorems which determine if a number is either prime or carmichael very quickly, and then other theorems which determine if a number is carmichael. Using these 2 theorems with wolfram, it should be pretty doable to check if a number is prime.
Does anyone here remember the details of basic number theory?
>>8076178
http://primes.utm.edu/lists/small/millions/
Since this is the largest known prime, you'd have to check more than 50,000,000 primes. But not that many, right?
>>8076188
t-t-traveling salesman heuristics?
>>8076188
Maybe we can use the theorems available to check for primality, mainly those involving carmichael numbers?
>>8076196
Would you mind linking to where I can find these theorems?
>>8076209
https://en.wikipedia.org/wiki/Primality_test#Miller-Rabin_and_Solovay-Strassen_primality_test
See: Fermat Test and Miller-Rabin Test here.
But I had a textbook that went into far more detail and explained how to fairly quickly determine if a number is prime. And that textbook is available (apparently as a free download) right here: http://www.e-booksdirectory.com/details.php?ebook=9362
>>8076225
I can see how this would make it easier, but I still think that it would be extremely hard to work with a number like this in general. It just seems extremely impractical to have a person do this.
>>8075546
>add one
>to an odd number
>to make a prime
>>8076252
works with 1
>>8076252
Nah. Then you just keep on adding one until it isn't. Although, that would probably take a very long time with numbers that large.
I found a constant [math]\phi[/math] such that the floor of 2^p^[math]{\phi}[/math]-1 is a prime if [math]2^p-1[/math] is a prime. Unfortunately, I seem to have forgotten it ...
>>8075511
its not because 74207281 is not a power of two
http://math.stackexchange.com/questions/532257/prove-if-prime-can-be-written-as-2n1-n-2k?lq=1
>>8076127
Prime numbers are the reason you can post here anonymously
>>8076252
He's adding two, smartass.
>>8075368
The product of all the primes from 2 to that one plus one.
>>8075993
Prove me wrong
>>8075368
They also ship to Somalia, and Syria.
>>8076339
2*3*5*7*11*13+1 is not prime
>>8076150
Bro, we don't have a list of every prime smaller than this number. In fact, only a very small fraction of all of the primes smaller than this number have ever been written down or saved on a computer.
Continuing from my original post here: >>8076473
in response to >>8076150.
The number of primes less than n is given by the function pi(n), which is approximated by x/(log(x)-1).
So we have approximately this many primes smaller than 2^74207281-1 :
pi(2^74207281-1) = (2^74207281-1)/(log(2^74207281-1)-1) =
approximately 10^10^7.3 = 10^73000000.
The number of atoms in the universe is roughly 10^80.
So if every atom in the universe contained a another universe, and in each of the atoms in these universes contained a computer with a harddrive as big as the universe, we would still be a LONG FUCKING WAY OFF from having enough disk space to create a list of the primes less than 2^74207281-1.
>>8076515
Nice
>>8076429
You're right, my bad. I thought Euclid's proof produces a new prime, but that's not the case.
why is it -1?
why cant they just write 1 to the power of 7427281 instead?
>>8077073
https://en.wikipedia.org/wiki/Freshman%27s_dream
?
1 + p_1 * ... * p_n
where each p is a known prime :^)
>>8077185
B-but [math]1 \,+\, 2 \,\times\, 7 \,=\, 1 \,+\, 14 \,=\, 15 \,=\, 3 \,\times\, 5[/math] is not a prime. :^)
>>8075368
Are we talking about integer primes specifically or prime ideals in general?
>>8075368
2 ^ (74207283) - 1
>>8077082
I hope this is in reference to high school freshmen, not undergraduate.
>>8077475
You don't meet enough freshmen.
>>8076367
This was a terrible, terrible pun.
>>8076515
Lol btfo me.
Thank you though, that was extremely informative.
>>8077082
Ahahah this is the actual name for this??
My abstract algebra teacher kept calling it the Freshman's Dream when he taught us this but I thought he had just made up that name. Seeing it really is the name is funny.
>>8077420
Just integer primes. Good catch though, that was my mistake. I should have been more specific.
INTEGER PRIMES.
>>8077470
Prove it.
>>8077470
74207283 isn't prime, try again
do we know what powers of 2 are not prime, can't we just do process of elimination
>>8077750
If [math]n[/math] is not prime then [math]2^n-1[/math] is not prime, but if [math]n[/math] is prime then [math]2^n-1[/math] is not necessarily prime.
>>8077757
But if it's not a Carmichael number, which we can check, then it is prime. Or something like that..
>>8077768
There are plenty of ways to check if a number is prime, and none of them are fast
>>8077783
2^a and 2^b could be two powers we know primes always occur between, no matter how big the number is, to be a little more specific. in all 2 digit numbers, there is at least one prime between every multiple of 10, extend the argument to powers of 2. it's obviously crude but it at least gives us a range
[math]2^{12266630448546421643300487969833547056583737115571318031747525873747317442466939353786593187413445779369660586829554677309690307702941187875462163578615512023214567560391499261}-1[/math]
Prove me wrong faggots
>>8077843
Can you explain the basis for this finding? I am curious.
>>8077859
That exponent is prime, so it could be a Mersenne prime, although probably not.
Take that prime, multiply it by two and add one
>>8077878
It would be divisible by 3
>>8077413
yer supposed to take all known primes up to n :^)
[math]2^{2^{1226663044854642164330048796980391499261}-1}-1[/math]
This is a prime. Prove me wrongs faglets
>>8078965
[math]23[/math] divides [math]1226663044854642164330048796980391499261[/math], therefore [math]2^{23}-1[/math] divides [math]2^{1226663044854642164330048796980391499261}-1[/math], therefore [math]2^{2^{23}-1}[/math] divides [math]2^{2^{1226663044854642164330048796980391499261}-1}-1[/math].
>>8079122
Typo, that should have been [math]2^{2^{23}-1}-1[/math].
>>8076131
It's up to you to prove that
>>8077750
[math]2^n[/math] is only prime for all [math]0\le n \lt 2[/math].
:^)
>>8079218
[math]2^n[/math] isn't prime for [math]n=0[/math]
>>8079223
oops
[math]0\lt n \lt2[/math]
>>8079232
[math]2^n[/math] isn't prime for [math]n=1.3[/math]
>>8076252
He's adding 1 to a number that's one more than a prime.
>>8079235
where [math]n\, \epsilon\, \mathbb{Z}[/math]
lol
>>8079243
assume [math]p[/math] to be a prime where [math]p \gt 2[/math]. Then, obviously, [math]p[/math] is odd.
So, following the algorithm, examine [math]p+1+1=p+2[/math], which is also odd. Assume, for the sake of argument, [math]p+2[/math] is not prime. By the algorithm, add [math]1[/math] to [math]p+2[/math]. Since [math]p+2[/math] is odd, [math]p+2+1[/math] is even. Even integers greater than 2 are not prime, therefore, the algorithm fucking sucks. [math]\blacksquare[/math]
>>8079249
>\epsilon \mathbb Z
>>8076367
>>8075368
I will now attempt to prove there are infinitely many twin primes:
1. There are infinitely many primes
2. If x is the product of all primes less than p, then x+1 and x-1 are both prime.
3. X+1-(x-1)=2
4.there are infinitely many x
5. QED
>>8080704
>product of all primes
>infinitely many primes
>a number
uh ok
>>8080731
Your lack of reading comprehension is worse than the flawed logic of that proof.
\mathbb COCK
>>8080704
>If x is the product of all primes less than p, then x+1 and x-1 are both prime.
2*3*5*7=210
209=11*19
>>8080762
Bro, if this proof was real, every integer could be proven prime.
>>8080704
Line two seems untrue, other than that good work
>>8075513
This.
Technically any computer could do this on a given time scale
>>8077937
It still wouldn't always make a prime.
2*3*5*7-1=209=11*19
>tfw you found the next prime number but forgot it
