Perfect number
Ancient mathematicians made many assumptions about perfect numbers based on the four they knew. Most of the assumptions were wrong. One of these assumptions was that since 2, 3, 5, and 7 are precisely the first four primes, the fifth perfect number would be obtained when n = 11, the fifth prime. However, 211 - 1 = 2047 = 23 × 89 is not prime and therefore n = 11 does not give a perfect number. Two other wrong assumptions were: