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.

A shard of smooth bone etched with irregular marks dating back 20,000 years puzzled archaeologists until they noticed something unique – the etchings, lines like tally marks, may have represented ...