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UID:6fedbb8025e9912c0f78091ad65411d4
CATEGORIES:Experimental Mathematics Seminar
CREATED:20250825T133607
SUMMARY:A heuristic link between divisor counts and prime densities in sequences
LOCATION:https://rutgers.zoom.us/j/95103383827   password: 6564120420
DESCRIPTION:I introduce a heuristic principle I call "probabilistic continuation" and c
 onjecture a striking asymptotic equivalence: the density of primes in a wel
 l-behaved integer sequence appears to match a structural ratio derived from
  the divisor counts of its terms. The appeal of this conjecture is practica
 l. Determining prime densities usually demands heavy analytic machinery (as
  in the Prime Number Theorem), whereas the associated divisor ratio is far 
 easier to evaluate. If the conjecture is correct, this ratio could thus pro
 vide a simpler proxy for fundamental density measures. I will present the m
 ain conjecture, show its consistency with classical results (PNT, PNT in ar
 ithmetic progressions, prime distribution in quadratic-residue sequences), 
 and discuss its coherence with Hardy-Littlewood-type conjectures\n
X-ALT-DESC;FMTTYPE=text/html:<p>I introduce a heuristic principle I call "probabilistic continuation" an
 d conjecture a striking asymptotic equivalence: the density of primes in a 
 well-behaved integer sequence appears to match a structural ratio derived f
 rom the divisor counts of its terms. The appeal of this conjecture is pract
 ical. Determining prime densities usually demands heavy analytic machinery 
 (as in the Prime Number Theorem), whereas the associated divisor ratio is f
 ar easier to evaluate. If the conjecture is correct, this ratio could thus 
 provide a simpler proxy for fundamental density measures. I will present th
 e main conjecture, show its consistency with classical results (PNT, PNT in
  arithmetic progressions, prime distribution in quadratic-residue sequences
 ), and discuss its coherence with Hardy-Littlewood-type conjectures</p>
CONTACT:Benoit Cloitre (independent researcher)
DTSTAMP:20260830T011122
DTSTART;TZID=America/New_York:20250918T170000
DTEND;TZID=America/New_York:20250918T180000
SEQUENCE:0
TRANSP:OPAQUE
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