What is bounded gaps between primes?
A prime gap is the difference between two successive prime numbers. The n-th prime gap, denoted gn or g(pn) is the difference between the (n + 1)-th and the n-th prime numbers, i.e.
What is the average gap between prime numbers?
For over a century, mathematicians have understood how the primes taper off on average: Among large numbers, the expected gap between prime numbers is approximately 2.3 times the number of digits; so, for example, among 100-digit numbers, the expected gap between primes is about 230.
What is the largest prime gap?
On the one hand there’s all these reports of the largest prime gap between all numbers proven to be < 246. On the other hand, I read reports of the largest known prime number gap being 1476.
Are all prime gaps even?
All primes other than 2 are odd, hence gap between them is even (as difference of two odd numbers is always even).
What is the maximum difference between two primes?
There is only one distinct prime number so the maximum difference would be 0.
What is successive prime numbers?
So, the distance between any two prime numbers in a row (called successive prime numbers) is at least 2. In our list, we find successive prime numbers whose difference is exactly 2 (such as the pairs 3,5 and 17,19).
How do you calculate prime gap?
pn+1 = pn + g(pn) + 1. That is, g(pn) is the (size of) gap between pn and pn+1. By the prime number theorem we know there are approximately n/log(n) (natural log) primes less than n, so the “average gap” between primes less than n is log(n).
How fast do primes grow?
So if the computing power available for seeking primes doubles every k months, then the size of the largest known prime should double every 3k months. The slope 0.079 (over past 60 years) corresponds to doubling the digits every 3.8 years, or 46 months.
What is the maximum difference between the two consecutive prime numbers between 1 and 100?
Largest prime number below 100 is 97 and smallest prime number is 2, hence the difference is 95.
What are the largest twin primes known today?
Large twin primes As of September 2018, the current largest twin prime pair known is 2996863034895. 21290000 ± 1, with 388,342 decimal digits. It was discovered in September 2016. There are 808,675,888,577,436 twin prime pairs below 1018.
Is 31 a Mersenne prime?
, 3, 5, 7, 13, 17, 19, 31, 61, 89, (OEIS A000043). Mersenne primes were first studied because of the remarkable properties that every Mersenne prime corresponds to exactly one perfect number.