It deals with "lumpers" and "splitters," and a possible trinomial nomenclature.
"More Letters of Charles Darwin" by Charles Darwin
The use of the trinomial here is arbitrary.
"The Amphibians and Reptiles of Michoacán, México" by William E. Duellman
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When searching for irreducible trinomials of degree r , we can assume that s ≤ r/2, since xr + xs + 1 is irreducible iff the reciprocal polynomial xr + xr−s + 1 is irreducible.
The great trinomial hunt
Over al l trinomials xr + xs + 1 of degree r over GF(2), the probability πd that a trinomial has no non-trivial factor of degree ≤ d is at most c/d, where c is an absolute constant and 1 < d ≤ r/ ln r .
The great trinomial hunt
An upper bound of r on d would probably be incorrect, since it would imply at most c irreducible trinomials of degree r , but we expect this number to be unbounded.
The great trinomial hunt
If the trinomials that have factors of degree less than log2 (r) are excluded by sieving, then by Assumption 1 we are left with O(r/ log r) trinomials to test.
The great trinomial hunt
They found one primitive trinomial; however they missed the trinomial x859433 + x170340 + 1, because of a bug in their sieving routine.
The great trinomial hunt
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