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It’s a result only a mathematician could love. Researchers hoping to get ‘2’ as the answer for a long-sought proof involving pairs of prime numbers are celebrating the fact that a mathematician has wrestled the value down from infinity to 70 million.
“That’s only [a factor of] 35 million away” from the target, quips Dan Goldston, an analytic number theorist at San Jose State University in California who was not involved in the work. “Every step down is a step towards the ultimate answer.”
A prime number is a positive integer greater than 1 that is only divisible by 1 and itself. In other words, it has exactly two factors.
To prove that two numbers are prime, you need to show that they have no factors other than 1 and themselves. This can be done by testing all possible factors, or by using the Sieve of Eratosthenes method.
A pair of prime numbers is two prime numbers that are consecutive and have a difference of 2. For example, 3 and 5, or 41 and 43, are both pairs of prime numbers.
To prove that a pair of numbers is a pair of prime numbers, you need to show that both numbers are prime and that their difference is 2. This can be done by using any method of proving primality, such as testing factors or using a primality test algorithm.
Pairs of prime numbers have a special significance in mathematics because they are the only known consecutive pair of primes with a difference of 2. This has been a topic of interest for mathematicians for centuries, and although many pairs of primes have been found, it is still unknown if there are an infinite number of them.