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Happy New Year! The number 2026 has two factors: 2 and 1013. I wondered “is 1013 prime?” and, for fun, “can I solve this in my head?” (e.g. no calculator, computer, or pen and paper). If 1013 is not prime, then it is composite and must have at least one odd prime factor ≤ ⌊√1013⌋. (We know the factor – if it exists – is odd because factors of odd composites are…
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