Mathematicians Discover Prime Conspiracy
A previously unnoticed property of prime numbers seems to violate a longstanding assumption about how they behave.
Two mathematicians have uncovered a simple, previously unnoticed property of prime numbers â€” those numbers that are divisible only by 1 and themselves. Prime numbers, it seems, have decided preferences about the final digits of the primes that immediately follow them. Among the first billion prime numbers, for instance, a prime ending in 9 is almost 65 percent more likely to be followed by a prime ending in 1 than another prime ending in 9.
...The discovery is the exact opposite of what most mathematicians would have predicted, said Ken Ono, a number theorist at Emory University in Atlanta. When he first heard the news, he said, â€œI was floored. I thought, â€˜For sure, your programâ€™s not working.â€™â€
This conspiracy among prime numbers seems, at first glance, to violate a longstanding assumption in number theory: that prime numbers behave much like random numbers. Most mathematicians would have assumed, Granville and Ono agreed, that a prime should have an equal chance of being followed by a prime ending in 1, 3, 7 or 9 (the four possible endings for all prime numbers except 2 and 5).