When it came to Marlborough College, Davenport, aged 16, discovered that, although it was ostensibly a six-digit computer, the microcode had access to a 12-digit internal register to do multiply/divide.

He used this to implement Draim's algorithm from his father Harold Davenport's book, The Higher Arithmetic, and tested eight-digit numbers for primality.

[6] Between school and university, Davenport worked in a government laboratory for nine months, again writing and using multiword arithmetic, but also using number theory to solve a problem in hashing, which was published.

[11] Davenport was awarded the Honorary Degree of Doctor of Science in September 2019 by the West University of Timişoara, Romania.

From January to June 2017 Davenport was a Fulbright CyberSecurity Scholar at New York University,[12] and maintained a blog[13] over the same period.