ITT: We break the world record

That's a multiple of 3

en.wikipedia.org/wiki/Prime_number#Applications

>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

I'll give it a shot:
[math] 2^{74207281} + 3 [/math] may be prime.

Maybes are meaningless.

>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?

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?

Read: en.wikipedia.org/wiki/Mersenne_prime

So, in other words, it's mostly to study math.

How do you know it's a twin prime?

>Like what's the likely distance between prime numbers at this scale?
that is a very good question

Didn't it take months to find this though, with lots of computing power.

Someone use this: en.wikipedia.org/wiki/Prime_number_theorem

the prime number theorem, to find the likely distance between primes at this level.

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.

>that is a very good question
OK.

>I have a pen and paper and I understand inverse multiplication.

It's a bit more complicated than that user. 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.

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..?

So why wouldn't this: work as a solution?

Rather than factoring by means of sieves, we can check for primality fairly quickly.

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?

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?

t-t-traveling salesman heuristics?

Maybe we can use the theorems available to check for primality, mainly those involving carmichael numbers?

Would you mind linking to where I can find these theorems?

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: e-booksdirectory.com/details.php?ebook=9362

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.

>add one
>to an odd number
>to make a prime

works with 1

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 ...

its not because 74207281 is not a power of two
math.stackexchange.com/questions/532257/prove-if-prime-can-be-written-as-2n1-n-2k?lq=1

Prime numbers are the reason you can post here anonymously

He's adding two, smartass.

The product of all the primes from 2 to that one plus one.

Prove me wrong

They also ship to Somalia, and Syria.

2*3*5*7*11*13+1 is not prime

By the prime number theorem, if N is a large number and x~N then the probably of x being prime is around 1/ln(N).

In this case:

ln(2^74207281)=74207281*ln(2) ≈ 51436567
So the probability of a random number in the range to be prime is about 0.00000001944, or 0.000001944%.

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: in response to .

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.

Nice

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?

en.wikipedia.org/wiki/Freshman's_dream
?

1 + p_1 * ... * p_n
where each p is a known prime :^)

B-but [math]1 \,+\, 2 \,\times\, 7 \,=\, 1 \,+\, 14 \,=\, 15 \,=\, 3 \,\times\, 5[/math] is not a prime. :^)

Are we talking about integer primes specifically or prime ideals in general?

2 ^ (74207283) - 1

I hope this is in reference to high school freshmen, not undergraduate.

You don't meet enough freshmen.

This was a terrible, terrible pun.

Lol btfo me.

Thank you though, that was extremely informative.

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.

Just integer primes. Good catch though, that was my mistake. I should have been more specific.

INTEGER PRIMES.

Prove it.

74207283 isn't prime, try again

do we know what powers of 2 are not prime, can't we just do process of elimination

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.

But if it's not a Carmichael number, which we can check, then it is prime. Or something like that..

There are plenty of ways to check if a number is prime, and none of them are fast

>not necessarily

do you have a range for this, maybe an interval, i.e. has to be between a and b, such that a has xyz properties and b has zyx properties etc.

why aren't they fast? why can't we at least approximate, or get intervals quickly?

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

Can you explain the basis for this finding? I am curious.

That exponent is prime, so it could be a Mersenne prime, although probably not.

Take that prime, multiply it by two and add one

It would be divisible by 3

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

[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].

Typo, that should have been [math]2^{2^{23}-1}-1[/math].

It's up to you to prove that

[math]2^n[/math] is only prime for all [math]0\le n \lt 2[/math].

:^)

[math]2^n[/math] isn't prime for [math]n=0[/math]

oops

[math]0\lt n \lt2[/math]

[math]2^n[/math] isn't prime for [math]n=1.3[/math]

He's adding 1 to a number that's one more than a prime.

where [math]n\, \epsilon\, \mathbb{Z}[/math]

lol

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]

>\epsilon \mathbb Z

...

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

>product of all primes
>infinitely many primes
>a number
uh ok

Your lack of reading comprehension is worse than the flawed logic of that proof.

\mathbb COCK

>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

Bro, if this proof was real, every integer could be proven prime.

Line two seems untrue, other than that good work

This.

Technically any computer could do this on a given time scale

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