The Prime Glossary states:
In a 1992 article, Samuel Yates coined the name gigantic prime for any prime with 10,000 or more decimal digits (he had also coined the term titanic primes a decade earlier).
But the annotation suggests that they were defined as primes with over rather than at least 10,000 digits:
Here Yates defines primes with more than 10,000 digits to be gigantic primes. Actually Yates suggested this as a name for those with over 5,000 digits; but the list was growing so fast that when the editor asked me to revise this article after Yates death I changed it to 10,000.
Can anybody say whether primes with exactly 10,000 digits are gigantic according to the original article?
S. Yates, "Collecting gigantic and titanic primes," J. Recreational Math., 24:3 (1992) 193--201.
The wikipedia page gives the following definition: A gigantic prime is a prime number with at least 10,000 decimal digits. It seems that the other statement in the prime glossary, namely "more than $10000$ digits" is wrong, as we know that the smallest gigantic prime is given by $$ p=10^{9999}+33603, $$ which has exactly $10000$ digits. Of course, a final proof, that this is what Yates has written, can only be obtained by consulting his article (which can be ordered in a university library).