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Reading the Wikipedia entry linked, I'd have to say that this is likely not the one the OP read. Generation ship is about the only "connection" I can see.
@JordanStefanelli The Country Code is the first part of a phone number, when used. The "exchange" is the first three digits in a 7-digit number for US phone numbers. In the exchange for US phone numbers anything in the 000-199 range is not supported. They are currently reserved for future expansion if needed. The Country Code and the exchange are totally different parts of a the number and a 1 being supported in one does not mean it is supported in another part of the number plan.
@templerman It proves nothing but it does suggest they were there and just not in the plot. As to lack of markings for them just remember the era when TOS first ran. Critical analysis by fans was not a "thing" back then. They were much more concerned with social reactions than fans. Imagine the nation's reaction to a white Capt. kissing his black communications officer in the mid-60's!
The exchange beginning with a "1" is fictitious by default, as such exchanges are not yet allowed in North America. So, it will get the given message anyway. However, is it possible that there is some other Easter Egg in the number using cipher techniques? Or in relation to something else in the movie, or its cast?