Any two 200 digit primes will do it
Without knowing all the 200 digit primes, I can't say whether or not that is a true statement. I wouldn't assume it is sufficient, however. The square root of 10^399 is a little greater than this 200 digit number:
3162277660168379331998893544432718533719555139325216826857504852792594
+438639238221344248108379300295187347284152840055148548856030453880014
+6905195967001539033449216571792599406591501534741133394841240
So, if there are two primes between 10^199 and that number, then there will be two 200 digit primes whose product is not a 400 digit number.
-sauoq
"My two cents aren't worth a dime.";
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