During 1871–1881, he was Instructor in Mathematics at the Thomason Civil Engineering College, Roorkee.
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Upon returning to the United Kingdom in 1881, he continued teaching at military institutes in Chatham, Dublin and Shorncliffe.
Allan J.C. Cunningham and Woodall gathered together all that was known about the primality and factorization of such numbers and published a small book of tables.
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The project is named after Allan Joseph Champneys Cunningham, who published the first version of the table together with Herbert J. Woodall.