When both n and n+12 are products of two distinct primes, the jump-12 equations force n=p(p+8) with (p,p+2,p+6,p+8) prime; prime powers never work.
Prove or Disprove. 100 Conjectures from the OEIS
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Presented here are over one hundred conjectures ranging from easy to difficult, from many mathematical fields. I also summarize briefly methods and tools that have led to this collection.
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Prime Quadruplets and Jump Conditions on Arithmetic Functions
When both n and n+12 are products of two distinct primes, the jump-12 equations force n=p(p+8) with (p,p+2,p+6,p+8) prime; prime powers never work.