When using LFSR as a psuedo-randon number generator an important subset of possible feedback settings are those which produce what are known as maximal length LFSR's which will produce a cyclic byte pattern of 2^N-1 bytes before repeating,the generator polynomials are prime over the field in question,so in the following examples to produce a maximal length LFSR 8 bits long the polynomial is X^7+X^1+1 Bit0 would be generated by Bit7 XOR BIT1.The following list is all the prime polynomials over GFn for register lengths upto 64 bits.


X^2 + X^1 + 1
X^3 + X^1 + 1
X^4 + X^1 + 1
X^5 + X^2 + 1
X^6 + X^1 + 1
X^7 + X^1 + 1
X^8 + X^6 + X^5 + X^1 + 1
X^9 + X^4 + 1
X^10 + X^3 + 1
X^11 + X^2 + 1
X^12 + X^7 + X^4 +X^3 + 1
X^13 + X^4 + X^3 + X^1 + 1
X^14 + X^12 + X^11 + X^1 + 1
X^15 + X^1 + 1
X^16 + X^5 + X^3 + X^2 + 1
X^17 + X^3 + 1
X^18 + X^7 + 1
X^19 + X^6 + X^5 + X^1 + 1
X^20 + X^3 + 1
X^21 + X^2 + 1
X^22 + X^1 + 1
X^23 + X^5 + 1
X^24 + X^4 + X^3 + X^1 + 1
X^25 + X^3 + 1
X^26 + X^8 + X^7 + X^1 + 1
X^27 + X^8 + X^7 + X^1 + 1
X^28 + X^3 + 1
X^29 + X^2 + 1
X^30 + X^16 + X^15 + X^1 + 1
X^31 + X^3 + 1
X^32 + X^28 + X^27 + X^1 + 1
X^33 + X^13 + 1
X^34 + X^15 + X^14 + X^1 + 1
X^35 + X^2 + 1
X^36 + X^11 + 1
X^37 + X^12 + X^10 + X^2 + 1
X^38 + X^6 + X^5 + X^1 + 1
X^39 + X^4 + 1
X^40 + X^21 + X^19 + X^2 + 1
X^41 + X^3 + 1
X^42 + X^23 + X^22 + X^1 + 1
X^43 + X^6 + X^5 + X^1 + 1
X^44 + X^27 + X^26 + X^1 + 1
X^45 + X^4 + X^3 + X^1 + 1
X^46 + X^21 + X^20 + X^1 + 1
X^47 + X^5 + 1
X^48 + X^28 + X^27 + X^1 + 1
X^49 + X^9 + 1
X^51 + X^16 + X^15 + X^1 + 1
X^52 + X^3 + 1
X^53 + X^16 + X^15 + X^1 + 1
X^54 + X^37 + X^36 + X^1 + 1
X^55 + X^24 + 1
X^56 + X^22 + X^21 + X^1 + 1
X^57 + X^7 + 1
X^58 + X^19 + 1
X^60 + X^1 + 1
X^61 + X^16 + X^15 + X^1 + 1
X^62 + X^57 + X^56 + X^1 + 1
X^63 + X^1 + 1