--%>
Assignment Help - homework help

State Prime number theorem

Prime number theorem: A big deal is known about the distribution of prime numbers and of the prime factors of a typical number. Most of the mathematics, although, is deep: while the results are often not too hard to state, the proofs are often difficult. We will introduce one fundamental and extremely significant theorem about the distribution of prime numbers. (Its proof is one of the difficult ones!)

Let x be any positive number. We denote by Π (x) the number of prime numbers less than or equal to x. The prime number theorem was conjectured by Gauss in the year 1791 (at the age of 14!), but was not proved until 1896, when it was proved independently through Jacques Hadamard and Charles de la Vallee Poussin.

982_prime number.jpg

(Remember that ln x denotes the natural logarithm of x: ln x = loge x.)

   Related Questions in Mathematics

  • Q : First-order formulas over the

    Consider the unary relational symbols P and L, and the binary relational symbol On, where P(a) and I(a) encode that a is apoint and a (sraight) line in the 2-dimensional space, respectively, while On(a,b) encodes  that a is a point, b is a line, and o lies on b.

    		•
  • Q : Theorem-G satis es the right and left

    Let G be a group. (i) G satis es the right and left cancellation laws; that is, if a; b; x ≡ G, then ax = bx and xa = xb each imply that a = b. (ii) If g ≡ G, then (g-1)

    		•
  • Q : Uniform scaling what is uniform scaling

    what is uniform scaling in computer graphic

    		•
  • Q : What is the probability that the film

    T.C.Fox, marketing director for Metro-Goldmine Motion Pictures, believes that the studio's upcoming release has a 60 percent chance of being a hit, a 25 percent chance of being a moderate success, and a 15 percent chance of being a flop. To test the accuracy of his op

    		•
  • Q : Set Theory & Model of a Boolean Algebra

    II. Prove that Set Theory is a Model of a Boolean Algebra The three Boolean operations of Set Theory are the three set operations of union (U), intersection (upside down U), and complement ~.  Addition is set

    		•
  • Q : Statistics math Detailed explanation of

    Detailed explanation of requirements for Part C-1 The assignment states the following requirement for Part 1, which is due at the end of Week 4: “Choose a topic from your field of study. Keep in mind you will need to collect at least [sic] 3- points of data for this project. Construct the sheet y

    		•
  • Q : Problem on Fermats method A public key

    A public key for RSA is published as n = 17947 and a = 3. (i) Use Fermat’s method to factor n. (ii) Check that this defines a valid system and find the private key X.

    Q : The mean of the sampling distribution

    1. Caterer determines that 87% of people who sampled the food thought it was delicious. A random sample of 144 out of population of 5000 taken. The 144 are asked to sample the food. If P-hat is the proportion saying that the food is delicious, what is the mean of the sampling distribution p-hat?<

    		•
  • Q : How to calculate area of pyramid

    Calculate area of pyramid, prove equation?

    		•
  • Q : Numerical solution of PDE i want you to

    i want you to solve this assignment. this consist of two parts theoretical and coding. the code has to be created by you. no modified or copying code. you have to mention the exact solution and the proportion error. also you have to explain the sketch that you get from the code. these information

    		•