# primes

1. ### Porve the sum of twin primes is divisible by 12

Show that the sum of twin primes is divisible by 12, for all primes > 3. Proof. Let p = 4k+1, then p+p+2 = 8k+4, so it is divisible by 4. Now, how do I get it to be divisible by 3? Thanks.
2. ### Table the firts 50 twin primes in Mathematica

I want to know how I find, calculate (make a list in Mathematica) for the firts 50 twin primes. If p is a prime and p+2 is a prime they called twin primes. Anybody who can tell me to programing the program Wolfram Mathematica? I have come this far, so long: 1) I make a new empty list, that...
3. ### Primes more and more sparse?

Is there some way to prove or show that the prime numbers occure more and more sparse at the number line?
4. ### Additions to primes that always yield composits

I have noticed that when adding positive integers to prime numbers, the result may or may not yield another prime number. There does not seem to be a pattern as to when an addition yields another prime. However, there is a set of numbers that does not appear to ever yield another prime when...
5. ### Finding all primes P

Can someone help me with how to go about this problem? Find all primes p such that: 8p^2 + 1 is also a prime, Thanks -Kate
6. ### infinite primes?

hello guys . question here how can i prove that there exists infinitely many primes p such that p = 3 mod 4. i have a little inkling as i know that if a,b=1 mod 4 then ab = 1 mod 4. Im guessing it would be along the lines of euclids theorem?
7. ### proof of inifinite primes

Could someone help me understand this proof? It says, by assumption, p=p_i for some i=1,2,3,...,n. It also says p_i | a and by assumption, p_i | a+1. It makes perfect sense if the p_i in the first statement and the p_i in the second are different values of i. But it declines this by saying...
8. ### Number Theory - Primes and Eulers equation

I really hate these types of questions. Can anyone help please?
9. S

### The temple of ancient primes

the underground temple of the lost civilisation of the ancient primes was recently discovered deep in a south american jungle. the jeys to the temple were discovered long ago. There are 25 of them, each one numbered with a different prime eless than 100. Each of the temple's doors has a lock...
10. ### Temple of Ancient Primes

Thye underground temple of the ancient primes was recently disovered deep in a South American jungle. The keys to the temple were discovered long ago. There are 25 of them, each one numbered with a different prime less than 100. Each of the temple's doors has a lock which requires a set of...
11. ### mersenne primes

I understand how you find these primes but how do you prove it? It seems so simple because you can just plug in numbers but thats not a mathematical proof. Prove that if (2^n)-1 is prime, then n is prime.
12. ### Primes in an Infinite Sequence

1.) Given the following infinite sequence: 9, 98, 987, 9876, ..., 987654321, 9876543219, 98765432198, ... What are all the primes? 2.) David has this unique social security number. The 9 digits in the social security number have the digits from 1 all the way through 9. The number also...
13. ### Find All Primes of a Number

Determine all of the primes that divide the number 100!
14. ### Complexity based proof of infinitude of Primes

In "Meta Math!" Greg Chaitin gives a sketch of a proof of the infinitude of primes based on complexity arguments. Here I want to give a fuller version of that proof. The gist of his proof is that if there were only a finite number of primes then as each number can be written as a product of...
15. ### Help to prove Primes

Hello, Can anyone please asssist with the following question: Prove that a positive integer a > 1 is a square if and only if in the canonical form of a all the exponents of the primes are even integers. I would surely appreciate it.
16. ### my last question-infinite number of primes

Please see the " Microsoft word" attachement. Thank you very much.