[bluesbassman]

[ QUOTE ]
philo, if there is a puzzle that starts like this:

2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59


how is the next number ANYTHING BUT 61?!?!?!? this must be the only unique answer to this puzzle. if you can come up with some math or logic that will yeild a different number, please show us now.

[/ QUOTE ]

Let F(n): R==>R be the function defined by:

F(n) = a0*(n^17) + a1*(n^16) + ... + a16*n + a17

where n is any real number, and {a0, a1, ... , a17} is a set of 18 real constant coefficients. It is easy to show by construction that there exist particular values of {a0, a1, ... , a17} which have the property:

F(1) = 2, F(2) = 3, F(3) = 5, ... , F(17) = 59, but that
F(18) <> 61. (i.e. F(18) does not equal 61.)

As Philo stated, there is no reason to favor the number 61 over F(18) as the next number in the sequence.