How large is the possible space between two consecutive prime numbers?

As of September 2017, the largest known prime gap with identified probable prime gap ends has length 6582144, with 216841-digit probable primes found by Martin Raab. This gap has merit M = 13.1829.

What is the prime number theorem used for?

The prime number theorem provides a way to approximate the number of primes less than or equal to a given number n. This value is called π(n), where π is the “prime counting function.” For example, π(10) = 4 since there are four primes less than or equal to 10 (2, 3, 5 and 7).

How do you prove a large number is prime?

The simplest primality test is trial division: given an input number, n, check whether it is evenly divisible by any prime number between 2 and √n (i.e. that the division leaves no remainder). If so, then n is composite. Otherwise, it is prime.

What is the meaning of consecutive prime numbers?

Define a series of consecutive prime numbers to be a series of numbers, each prime, in which there are no other prime numbers between them. These are not necessarily consecutive numbers themselves. For example, the numbers 5,7 and 11 are consecutive prime numbers, although they are not consecutive numbers.

Is there a relationship between prime numbers?

Prime numbers are numbers that can only be evenly divided by 1 and themselves, such as 5 and 17. If A and B are two such numbers and C is their sum, the ABC conjecture holds that the square-free part of the product A x B x C, denoted by sqp(ABC), divided by C is always greater than 0.

How do you determine whether a number is prime or not?

To find whether a larger number is prime or not, add all the digits in a number, if the sum is divisible by 3 it is not a prime number. Except 2 and 3, all the other prime numbers can be expressed in the general form as 6n + 1 or 6n – 1, where n is the natural number.