Noun
prime field (plural prime fields)
(algebra, field theory) A field that contains no proper subfields.
For example, the prime field is the smallest subfield of a field F containing both 0 and 1. It is either Q or the finite field with p elements, whence the name. Source: Internet
For the prime field case, this was broken in July 2009 using a cluster of over 200 PlayStation 3 game consoles and could have been finished in 3.5 months using this cluster when running continuously. Source: Internet
The hardest ECC scheme (publicly) broken to date had a 112-bit key for the prime field case and a 109-bit key for the binary field case. Source: Internet