Donnie Darko: The Third Perfect Number (496)

The numbers in Frank's warning are 28, 6, 42 and 12.

• 6 is the first perfect number → 2¹(2² − 1) = 6
• 28 is the (2)nd perfect number → 2²(2³ − 1) = 28

The (3)rd perfect number is 496 → 2⁴(2⁵ − 1) = 496

• 496 is a divisors of 1488:

(3) × 496 = 1488

1488 = (16×93)

Consider again the numbers (28, 6, 42, 12) in Frank's warning.

• Donnie Darko was filmed in 28 days matching the time that transpires in the film from the date of Frank's warning.
• 6, 42 and 12 are divisors of 3024.

In number theory a perfect number is a positive integer equal to the sum of its proper positive divisors excluding the number itself.

The divisors of 496 sum to 992.

The divisors of 3024 sum to 9920.

9920 has 28 divisors, 496 being one.

• (6×42×12) = 3024 = (11×11×11) + 1693
• 496 is the (3)rd perfect number and a divisor of 1488 → 496 × (3) = 1488 = (16×93)

The divisors of 1488 sum to 3968:

The divisors of 3024 sum to 9920:

3968 + 9920 = (28)×(496)