Literary Primes

Let a number be a literary prime if the both the number itself and the number of letters required to spell the number are prime.

English examples:
two, three, seven, twenty three, thirty seven, seventy nine, one hundred thirty one.

First Bullshit Conjecture: There are an infinite number of literary primes.

German examples:

elf (11), einunddreißig (31), einundvierzig (41)

Mandarin Chinese examples (pinyin):

èr (2), sān (3), qī (7)

Second Bullshit Conjecture: There does not exist a written language that does not have literary primes.

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