Around 1000 AD, the Islamic mathematician Ibn al-Haytham (Alhazen) found Wilson's theorem, characterizing the prime numbers as the numbers formula_1 that evenly divide formula_17. He also conjectured that all even perfect numbers come from Euclid's construction using Mersenne primes, but was unable to prove it. Another Islamic mathematician, Ibn al-Banna' al-Marrakushi, observed that the sieve of Eratosthenes can be sped up by testing only the divisors up to the square root of the largest number to be tested. Fibonacci brought the innovations from Islamic mathematics back to Europe. His book "Liber Abaci" (1202) was the first to describe trial division for testing primality, again using divisors only up to the square root.