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Blimey! I was able to figure it out.

for(p=1, 10000, for(y=1, 10000, for(z=1, 10000, if(y < z && 1 + p^y < 2*p^(2*y-z) && isprime(p),print(p,"   ",y,"   ",z)))))

It is a common mistake of mine. I keep forgetting the * to indicate multiplication.