primes

  1. T

    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. B

    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. TriKri

    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. W

    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. K

    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. J

    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. Tomato

    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. M

    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. Bartimaeus

    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. H

    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. F

    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. F

    Find All Primes of a Number

    Determine all of the primes that divide the number 100!
  14. CaptainBlack

    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. L

    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. J

    my last question-infinite number of primes

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

    Quadratic primes

    Question 1) Prove that there are infinitely many prime in Q[sqrt(d)] . Hint: It is almost identical to the proof that there are infinitely many prims in Z. Question 2) Find a prime factorization of 6 in Q[ sqrt(-1)] ? Hi Perfecthacker, Could you please teach me how to solve these...
  18. J

    Euclid's theorem and primes numbers

    Hi, How do I prove that if Pn is the n-th prime, then Pn < 2^(2^n) - using Euclid's theorem? Thanks.
  19. C

    Let P be the set of primes that divide 200!.

    Thanks for all the help you all have provided. Now, next question. I really just don't get it. Wish they would teach us this stuff in school... Let P be the set of primes that divide 200!. What is the largest integer k so that the set of primes that divides k! is equal to P?
  20. S

    For all primes greater than 3, p = 6k±1?

    is it true? what is the proof? I prefer a hint if it ain't difficult to prove. tnx :)