Only irreducible p(x) listed. The only known exception to one having a Fib. index of 2^k+-1 is p_1807. The Fibonacci index is indicated in parentheses. p(x) is self-conjugate if p(x)=p(x+1) (over GF(2)). We remark that f_5 is the *only* self-conjugate Fibonacci polynomial (this is a theorem). p_7:x^2 +x +1 (5) p_19:x^4 +x +1 (17) p_109:x^6 +x^5 +x^3 +x^2 +1 (63) p_361:x^8 +x^6 +x^5 +x^3 +1 (255) p_379:x^8 +x^6 +x^5 +x^4 +x^3 +x +1 (257) p_1807:x^10 +x^9 +x^8 +x^3 +x^2 +x +1 (205) p_1821:x^10 +x^9 +x^8 +x^4 +x^3 +x^2 +1 (1023) p_1891:x^10 +x^9 +x^8 +x^6 +x^5 +x +1 (1025) p_4645:x^12 +x^9 +x^5 +x^2 +1 (4095) p_4663:x^12 +x^9 +x^5 +x^4 +x^2 +x +1 (4097) p_4897:x^12 +x^9 +x^8 +x^5 +1 (4095) p_4915:x^12 +x^9 +x^8 +x^5 +x^4 +x +1 (4097)