Enigma 1092: A prime age
16 October 2017
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From New Scientist #2248, 22nd July 2000 [link]
Marge, April, May, June, Julia and Augusta have all celebrated their birthday today. They are all teenagers and with the exception of the one pair of twins their ages are all different.
Today, only Marge and April have ages which are prime numbers, but the sum of the ages of all the girls is also a prime number. On their birthday last year, only May and June had ages which were prime numbers, but again the sum of the ages of all the girls was a prime number. On their birthday two years before that, only May and Julia had ages which were prime numbers, but even then, the sum of the ages of all the girls was again a prime number.
How old is Augusta?