Ford's early work focused on the distribution of
Euler's totient function. In 1998, he published a paper that studied in detail the range of this function and established that
Carmichael's totient function conjecture is true for all integers up to 10^{10^{10}}. In 1999, he settled
Sierpinski’s conjecture on
Euler's totient function. In August 2014, Kevin Ford, in collaboration with
Green,
Konyagin and
Tao, resolved a
longstanding conjecture of
Erdős on large gaps between primes, also proven independently by
James Maynard. The five mathematicians were awarded for their work the largest Erdős prize ($10,000) ever offered. In 2017, they improved their results in a joint paper. He is one of the namesakes of the
Erdős–Tenenbaum–Ford constant, named for his work using it in estimating the number of small integers that have divisors in a given interval. ==Recognition==