 Most often, the number spiral is started with the number 1 at the center, but it is possible to start with any number, and the same concentration of primes along diagonal, horizontal, and vertical lines is observed.Starting with 41 at the center gives a diagonal containing an unbroken string of 40 primes (starting from 1523 southwest of the origin, decreasing to 41 at the origin, and increasing to 1601 northeast of the origin), the longest example of its kind.According to Gardner, Ulam discovered the spiral in 1963 while doodling during the presentation of "a long and very boring paper" at a scientific meeting.