id: 02370167
dt: j
an: 2007a.00249
au: Francis, Richard L.
ti: A mathematical paradise (The world of infinity). Pt. II.
so: Consortium, No. 89, 10-14 (2005).
py: 2005
pu: COMAP (Consortium for Mathematics and Its Applications), Bedford, MA
la: EN
cc: E60 F60
ut: cardinality; numbers sets; number theory; prime numbers
ci:
li:
ab: Author’s abstract: Many of the unsolved problems of today concern the
question ’How many?’ Various number sets are obviously finite, such
as the set of even primes, and some are just as evidently in the
infinite category. The latter encompasses such sets as the counting
numbers, the integers and the rationals. Others required a careful
analysis before the conclusion of infinitude was established. The
classical problem of the cardinality of the primes, resolved by Euclid
in the Elements, provides a well-known example. However, a vast
assortment of present day explorations continues to demand the
mathematician’s best efforts. Among these are the many conjectures
and failed attempts concerning prime number types (Mersenne primes,
Fermat primes, twin primes, and more).
rv: