Research Notes

Focused investigations of the Mersenne × primorial grid. Each note states its question, answer and evidence. The paper develops the central structure, primality criteria and fixed census. The catalogue reports the current proven primes; Explore the Grid computes individual values and displays verdicts from the published data.

Why exponent-sieve factors cannot be multiplied

Exact finite result. Shared exponent periods change the joint survival fraction. A two-prime example gives different answers on the two faces, although the product of individual survival fractions is identical.

Read the proof and reproduce the counts →

Decimal endings on both faces

Proved congruence classification. Why row 5 always ends in 09/11, which other rows and exponents share that pair, and how to determine the exact cycle for any number of decimal places. The first three rows have separate behavior.

Read the classification and proof →

Reading the results

For the distinction between exact finite results and heuristic prime frequencies, see the paper's density discussion.