06-27-2026, 07:07 PM
Mills' constant
Summary
William Harold Mills's Mills' constant is one of the most fascinating and mysterious numbers in number theory. It is a special mathematical constant with the remarkable property that taking the integer part of ($A^{3^n}$) always produces a prime number for every positive integer (n). Although Mills proved in 1947 that such a constant must exist, its exact value cannot be determined without relying on deep assumptions about the distribution of prime numbers, such as the Riemann hypothesis.
Assuming that hypothesis is true, the constant begins with approximately $1.30637788386308...$, generating the prime sequence $2, 11, 1361$, and increasingly enormous primes. Despite decades of research, Mills' constant remains an intriguing object of study because it beautifully links seemingly random prime numbers with a single fixed real number, and recent work has even established that the constant is irrational.
ARTICLE
Summary
William Harold Mills's Mills' constant is one of the most fascinating and mysterious numbers in number theory. It is a special mathematical constant with the remarkable property that taking the integer part of ($A^{3^n}$) always produces a prime number for every positive integer (n). Although Mills proved in 1947 that such a constant must exist, its exact value cannot be determined without relying on deep assumptions about the distribution of prime numbers, such as the Riemann hypothesis.
Assuming that hypothesis is true, the constant begins with approximately $1.30637788386308...$, generating the prime sequence $2, 11, 1361$, and increasingly enormous primes. Despite decades of research, Mills' constant remains an intriguing object of study because it beautifully links seemingly random prime numbers with a single fixed real number, and recent work has even established that the constant is irrational.
ARTICLE
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│ KONSTANTINOS MICHAILIDIS │
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│ KONSTANTINOS MICHAILIDIS │
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