Maxima of difference between Primes!
Let be seven distinct prime numbers such that the sum of two of is 800. Let be the difference between the largest and the smallest numbers among the seven primes. Find the largest possible value of .
The answer is 1594.
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1 solution
(sketch) Wlog a>b>c. Now a+b+c is the largest and b+c-a<c and so is the smallest. Hence, d=(a+b+c)-(b+c-a)=2a. But a<b+d<=800 and then a=797 works (as 800-797=3 is indeed a prime). Hence d=2*797=1594.