The smallest prime that is also a sum of primes beginning and ending with the digit seven (1531 = 7 + 727 + 797). Well, excluding the degenerate case of 7 by itself...



The smallest odd number that is not the sum of a prime and a power > 1 (!)

For examples:
1543 = 1511 + 2^5
1531 = 1523 + 2^3
1523 = 1459 + 8^2

... but no such equation for 1549.



As we all know, every number is interesting. I'm just pointing out some of the reasons why.

But yes, I did my master's in number theory very long ago. I studied under Gauss.



There are 98 million primes less than 2000000000, so we could be here for a while :-)


OK, I am new to this, but is there a simple test for a number being prime? The number obviously cannot end in an even number or with a five or a zero. So we eliminate testing division by 2, 4, 5, 6, 8, and 10 immediately. Any number divisible by 9 is also divisible by 3, so it seems the first tests are to find if the next number is divisible by 3, 7, 11, 13, 17, etc., to include other prime numbers as we progress. Does this make sense?

It seems that 1667 is the next number that passes these tests.

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