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A free neutron decays with a half-life of about 1013 seconds into a proton, an electron, and an antineutrino. [Hughes]

The average sea-level pressure on Earth is about 1013 millibars. [Webb]

2¹⁰¹³ + 3¹⁰¹³ + 5¹⁰¹³ + 7¹⁰¹³ is prime. [Opao]

The prime sum of p(i), where i takes the values of the 11 first Fibonacci numbers. [Gallardo]

In Marcus du Sautoy's book The Music of the Primes, while discussing Bertrand's postulate, he states that there are actually quite a lot of primes between 1009 and 2018, the first being 1013.