A triangular number can produce a prime if 1 is added or subtracted or 2 is added or subtracted.

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If a triangular number is even add or subtract 1; if odd, add or subtract 2. Count the number of primes found by subtraction and by addition and it appears that MORE are found by addition than by subtraction. A sample of the first 44 triangular numbers found 17 for subtraction and 26 for addition. Does this difference hold for more triangular numbers considered?