Twin primes are primes that are exactly two apart. For example, 41 and 43, are twin primes. (The two Bushes were twin prime presidents — I’m surprised nobody ever pointed that out!) Write a function twinprimes(primes) that takes as input a list of prime numbers and returns another list twins containing all the twin primes. Be sure to write your code in such a way that the list primes remains unaltered. (It is known that there are infinitely many prime...
Define in Scheme an infinite stream consisting of twin prime numbers. All primes ? with the property that ? + 2 or ? − 2 are also prime should be included, each one only once. Hint: Apply the Sieve of Eratosthenes.
Use the inclusion – exclusion principle to find the number of primes less than 24. Use the formula: N (?′??′?) = N - |??| - |??| + |?? ∩ ?? |
in the sieve of Eratosthenes for numbers less than 100, explain why after we cross our the multiples of 2 3 5 and 7 the remaining numbers are primes.
Use a Mathlab program using the while/for command and run it for the following exercise. 20. A twin primes is a pair of prime numbers such that the difference between them is2 (for example, 17 and 19). Write a computer program that finds all the twin primes between 10 and 500. The program displays the results in a two- column matrix in which each row is a twin prime. Do not use MATLAB's built-in function is prime. Use a Mathlab...
8. Define (n) to be the number of positive integers less than n and n. That is, (n) = {x e Z; 1 < x< n and gcd(x, n) = 1}|. Notice that U (n) |= ¢(n). For example U( 10) = {1, 3,7, 9} and therefore (10)= 4. It is well known that (n) is multiplicative. That is, if m, n are (mn) (m)¢(n). In general, (p") p" -p Also it's well known that there are relatively prime, then...
Prove that any triangulation where every triangle is acute (all angles are less than π/2) is Delaunnay.
4. Use quadratic reciprocity to find a congruence describing all odd primes for which 5 is a quadratic residue. 4. Use quadratic reciprocity to find a congruence describing all odd primes for which 5 is a quadratic residue.
1. Let A be 1 more than the product of the primes 3, 5, and 7. Factor A into a product of primes and check how many of 3, 5,7 are factors of A. 2. Make a list consisting of a few of your favorite primes and let B be 1 more than the product of these primes. Factor B into a product of primes and check how many of the primes on your list are factors of B.
How do I Write a program called primecount that generates primes up to 1000000000 using the sieve of Erastosthenes and then counts the number of primes less than or equal to each of the numbers 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000, and1000000000. The prime number theorem says that for large values of n, the number of primes less than or equal to n (π(n)) is approximately n / ln n. Print 4 columns, each in a field of...