Andrew R. Hands

Document Type

Honors Thesis


Grimm's Conjecture asserts that given any sequence of consecutive natural numbers, say n +1, n + 2,...,n + k for integers n and k. there exists k distinct primes, p1, p2,..., Pk, such that n + i is divisible by Pi, for all i = 1,2,..., k. A construction for graphical repres entations was demonstrated by setting each composite and each prime as a node and then drawing an edge between composite and prime nodes to indicate divisibility. Valuations and related works were used to prove properties of those sub-graphs. Algorithms were then explored to help with finding experimental results regarding minimal interval lengths for counterexamples. It was then shown given a known valuation for a particular node, valuations for many nearby if not all nodes could in turn be evaluated for the same prime. It was then shown Grimm's Conjecture holds for all k ≤ 31 and a new method for deriving a relationship between n and k was found.

Publication Date






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