pretty sure that "number" is the subject of the sentence. "of websites" is a prepositional phrase acting, I believe, as an appositive adjective.
But I am kinda rusty, grammar-wise...
Sorry, man. Per my linguist & grammarian daughter:
"In existential (“there is/are”) constructions, the subject of the verb is the dummy pronoun “there.” We can do a simple subject-verb inversion test to prove this. That is, when we use inversion to form a question from a “there is/are” statement, it is “there” (subject) and the verb that switch places, not the verb and something else. So the statement:
“There is/are an infinite number of really odd websites.”
Becomes the question:
“Is/are there an infinite number of really odd websites?” - The subject “there” and the verb “is/are” have switched places.
If we say that “an infinite number of really odd websites” is the subject and invert that and “is/are” instead, we can get a grammatical question but it means something different:
“Is/are an infinite number of really odd websites there?” - Here, “there” indicates location, not the existence of something.
Since the subject “there” is neither singular nor plural, we cannot use traditional-subject verb agreement.
Instead, to conjugate the verb, we must use the principle of proximity (verb agrees with the closest noun after it) or notional agreement (agreement based on intended meaning and/or what sounds most natural).
The principle of proximity would call for “is” in this example because the closest noun to the verb is the singular “an infinite number.”
But “are” might be preferred under notional agreement because it highlights the fact that there are multiple websites, and therefore “are” is probably a more accurate verb conjugation for the intended meaning of the sentence.
So, both “is” and “are” are grammatically correct for this example.
If this were not a “there is/are” statement (e.g., “An infinite number of really odd websites is/are available”), then technically the grammatical subject is the singular “an infinite number” and “of really odd websites” is a prepositional phrase describing the subject (which usually do not factor into subject-verb agreement). So it would be correct to use “is” to agree with “an infinite number.”
However, it would also be correct to use the principle of proximity/notional agreement here - since plural “websites” is the closest noun to the verb, “are” would be appropriate (principle of proximity), and again, if you want to emphasize that multiple websites exist, then “are” would also work under notional agreement. You see this frequently in constructions like, “A majority of the men were wearing hats” - where “were” agrees with plural “the men” and not singular “a majority.” Contrary to what some people might say, this is not grammatically incorrect."