must 'x' in g^x be a prime number

[ikuzar]

Hello,
I 'd like to know  :
1) if exponent x in g^x must be a great prime number. In some docs I saw, it
is said that x must b a GREAT number but no information about primality ..
2) May generation of 'x' run for hours like related here :
http://www.openssl.org/docs/crypto/DH_generate_parameters.html ( in NOTES)
Thanks for your help.