Albert Edward Ingham FRS (3 April 1900 – 6 September 1967) was an English mathematician.[4]

Albert Ingham
Albert Edward Ingham

(1900-04-03)3 April 1900
Died6 September 1967(1967-09-06) (aged 67)
Alma materTrinity College, Cambridge
AwardsSmith's Prize (1921)[1]
Fellow of the Royal Society[2]
Scientific career
InstitutionsUniversity of Cambridge
Doctoral studentsWolfgang Fuchs
C. Haselgrove
Christopher Hooley
Robert Rankin[3]
InfluencesJohn Edensor Littlewood[1]
Erdős Number: 1


Ingham was born in Northampton. He went to Stafford Grammar School and Trinity College, Cambridge.[1]


Ingham supervised the Ph.D.s of C. Brian Haselgrove, Wolfgang Fuchs and Christopher Hooley.[3] Ingham died in Chamonix, France.

Ingham proved in 1937[5] that if


for some positive constant c, then


for any θ > (1+4c)/(2+4c). Here ζ denotes the Riemann zeta function and π the prime-counting function.

Using the best published value for c at the time, an immediate consequence of his result was that

gn < pn5/8,

where pn the n-th prime number and gn = pn+1pn denotes the n-th prime gap.


  1. ^ a b c O'Connor, John J.; Robertson, Edmund F., "Albert Ingham", MacTutor History of Mathematics archive, University of St Andrews.
  2. ^ Burkill, J. C. (1968). "Albert Edward Ingham 1900-1967". Biographical Memoirs of Fellows of the Royal Society. 14: 271–286. doi:10.1098/rsbm.1968.0012.
  3. ^ a b Albert Ingham at the Mathematics Genealogy Project
  4. ^ The Distribution of Prime Numbers, Cambridge University Press, 1932 (Reissued with a foreword by R. C. Vaughan in 1990)
  5. ^ Ingham, A. E. (1937). "On the Difference Between Consecutive Primes". The Quarterly Journal of Mathematics: 255–266. Bibcode:1937QJMat...8..255I. doi:10.1093/qmath/os-8.1.255.