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ਕਦਮ ਦਰ ਕਦਮ

1. \sqrt{1000003} \approx 1000

   Only primes up to √1000003 need testing: any factor above it pairs with one below.

2. 1000003 \bmod 2 = 1

   2 does not divide 1000003.

3. 1000003 \bmod 3 = 1

   3 does not divide 1000003.

4. 1000003 \bmod 5 = 3

   5 does not divide 1000003.

5. 1000003 \bmod 7 = 4

   7 does not divide 1000003.

6. 1000003 \bmod 11 = 4

   11 does not divide 1000003.

7. 1000003 \bmod 13 = 4

   13 does not divide 1000003.

8. 1000003 \bmod 17 = 12

   17 does not divide 1000003.

9. 1000003 \bmod 19 = 14

   19 does not divide 1000003.

10. \vdots

    …and the same for every prime up to 1000 (168 primes checked).

11. \text{1000003 is prime}

    No prime up to the square root divides it, so it has no factors other than 1 and itself.

ਜਵਾਬ ਦਿਓ

\text{1000003 is prime}