Carl Gribble

Certified exact sums of primes over dyadic intervals via a ladder of generalized factorials

For S(m), the sum of primes in the dyadic window (m, 2m], the paper constructs a ladder of generalized factorials whose integer exponent sequences are Chebyshev polynomials rescaled to take integer values. The p-adic valuation at a window prime p equals the exponent polynomial Q_...

Prime counts and prime sums from multiplication tables: a self-similar formula system

A multiplication table whose entries are all at least 2 manufactures exactly the composite numbers; the primes are what the table cannot make. Carrying that observation to completion yields a three-line inductive formula family S_j computing prime counts (j = 0), prime sums (j =...

Recovering the primes in a dyadic interval from exact moments: two constructive routes and an obstruction theorem

Companion papers supply two exact moment channels for the primes in a dyadic window (m, 2m]: integer power sums produced from divisor-lattice data with no prime input, and weighted logarithmic moments produced from the primes below the window. This paper closes the circle: the ch...

Recovering the primes in a dyadic interval from exact moments: two constructive routes and an obstruction theorem

Companion papers supply two exact moment channels for the primes in a dyadic window (m, 2m]: integer power sums produced from divisor-lattice data with no prime input, and weighted logarithmic moments produced from the primes below the window. This paper closes the circle: the ch...

Certified exact sums of primes over dyadic intervals via a ladder of generalized factorials

For S(m), the sum of primes in the dyadic window (m, 2m], the paper constructs a ladder of generalized factorials whose integer exponent sequences are Chebyshev polynomials rescaled to take integer values. The p-adic valuation at a window prime p equals the exponent polynomial Q_...

Certified exact sums of primes over dyadic intervals via a ladder of generalized factorials

For S(m), the sum of primes in the dyadic window (m, 2m], the paper constructs a ladder of generalized factorials whose integer exponent sequences are Chebyshev polynomials rescaled to take integer values. The p-adic valuation at a window prime p equals the exponent polynomial Q_...

Recovering the primes in a dyadic interval from exact moments: two constructive routes and an obstruction theorem

Companion papers supply two exact moment channels for the primes in a dyadic window (m, 2m]: integer power sums produced from divisor-lattice data with no prime input, and weighted logarithmic moments produced from the primes below the window. This paper closes the circle: the ch...