The longest series of this kind known at present consists of forty prime numbers. It begins with 41, 43, 47, 53 … and ends with … 1373, 1447,1523,1601, a truly extraordinary sequence.

Prime numbers, fundamental to number theory and mathematics, have intrigued humans for millennia. Mersenne primes, of the form 2 p –1, are central to the search for large primes.

Informally, a positive counting number larger than one is prime if that number of dots can be arranged only into a rectangular array with one column or one row. For example, 11 is a prime number ...