Can prime numbers be perfect numbers?
Can prime numbers be perfect numbers?
Prime-perfect numbers appear to have been first considered by the second author, who proved [24] that every such number with two distinct prime factors is an even perfect number.
What is the relationship between prime numbers?
Prime numbers are numbers that can only be evenly divided by 1 and themselves, such as 5 and 17. The ABC conjecture makes a statement about pairs of numbers that have no prime factors in common, Peterson explained.
What is special about the number 2 when thinking about prime numbers?
The number 2 has only two whole number factors, 1 and itself. That’s pretty much it after this: The other numbers that are even up from two are all divisible by that number in some way. This is also known as the “oddest prime” because it’s the only prime number that’s even, so it’s also known as the odd one out.
Is 2 a Mersenne prime?
The exponents n which give Mersenne primes are 2, 3, 5, 7, 13, 17, 19, 31, (sequence A000043 in the OEIS) and the resulting Mersenne primes are 3, 7, 31, 127, 8191, 131071, 524287, 2147483647.
What is the pattern of prime numbers?
Now, however, Kannan Soundararajan and Robert Lemke Oliver of Stanford University in the US have discovered that when it comes to the last digit of prime numbers, there is a kind of pattern. Apart from 2 and 5, all prime numbers have to end in 1, 3, 7 or 9 so that they can’t be divided by 2 or 5.
What happens if you add two prime numbers together?
All prime numbers, with the exception of the number 2, are odd. As any two odd numbers added together creates an even number, the only way of creating a sum containing two prime numbers added together, that comes out as odd, you must do 2 added to any other prime number that exists. 2 and 3.
Are there infinitely many Mersenne primes?
Many fundamental questions about Mersenne primes remain unresolved. It is not even known whether the set of Mersenne primes is finite or infinite. The Lenstra–Pomerance–Wagstaff conjecture asserts that there are infinitely many Mersenne primes and predicts their order of growth.
What is the largest known Mersenne prime?
The largest known prime number (as of November 2018) is 277,232,917 − 1, a number with 23,249,425 digits. It was found by the Great Internet Mersenne Prime Search ( GIMPS ) in 2017.
How many Mersenne primes are known?
There are 49 known Mersenne primes from which the biggest exponent is 74 207 281. There are 303 128 primes less than 74 207 281.
What is known as a Mersenne prime number?
A Mersenne prime is any prime number that is a power of 2, minus 1. It is defined as Mn = 2n – 1, where n is any integer. For instance, the prime number 3 is a Mersenne prime, because it equals 2 2 – 1.
