MJC!
I was enthused and tried myself upto first 200 even integers when I first came to know the theorem when I was at age 12. Though I am a frequent visitor of that Wolfram site, I didn't come across this particular link. Thanks. In fact I saw a paper on the web which claims to have proved this theorem in Vedic Mathematics way. I went through it but it was well over my head.
When I was in my first year engineering, we were asked to write a computer program in Fortran for checking prime numbers:-( in the final examination. Yeah, God did bless me and I passed that exam.
Believe it or not : Goldbach's conjecture says any even number can be written as a sum of two prime numbers. Postulated in 16th century, nobody could, so far, prove it nor disproove it.