/Prime-Pattern

This is a list of some interesting primes with distinct patterns.

Wonderful Demlo Numbers (OEIS: A002477)

  1. $$11^2 + 10$$
  2. $$111^2 + 100$$
  3. $$1111^2 + 1000$$
  4. $$11111111^2 + 10000000$$
  5. $$11111111111111^2 + 10000000000000$$
  6. $$11111111111111111^2 + 10000000000000000$$
  7. $$1111111111111111111^2 + 1000000000000000000$$
  8. $$11111111111111111111^2 + 10000000000000000000$$
  9. $$111111111111111111111111111111^2 + 100000000000000000000000000000$$
  10. $$11111111111111111111111111111111111^2 + 10000000000000000000000000000000000$$
  11. $$1111111111111111111111111111111111111111111111111111^2 + 1000000000000000000000000000000000000000000000000000$$

Factorial-Sum Primes (My Idea)

  1. $$2!+1!$$
  2. $$3!+2!-1!$$
  3. $$4!+3!+2!-1!$$
  4. $$5!+4!+3!+2!-1!$$
  5. $$6!-5!+4!+3!+2!-1!$$
  6. $$7!-6!-5!+4!+3!+2!-1!$$
  7. $$8!-7!+6!-5!-4!-3!+2!-1!$$
  8. $$9!+8!-7!+6!-5!-4!-3!+2!-1!$$
  9. $$10!-9!+8!-7!+6!-5!+4!-3!+2!-1!$$
  10. $$11!+10!+9!-8!-7!+6!+5!-4!-3!+2!-1!$$
  11. $$12!+11!+10!-9!+8!+7!+6!+5!-4!+3!+2!-1!$$
  12. $$13!-12!+11!+10!+9!-8!-7!+6!+5!-4!-3!-2!+1!$$
  13. $$14!-13!-12!-11!+10!-9!-8!-7!+6!+5!+4!-3!+2!-1!$$
  14. $$15!+14!+13!+12!-11!+10!+9!+8!-7!+6!-5!+4!+3!-2!+1!$$
  15. $$16!+15!+14!-13!+12!-11!+10!+9!+8!-7!+6!-5!+4!+3!-2!+1!$$
  16. $$17!+16!+15!+14!-13!-12!+11!+10!+9!+8!-7!+6!-5!+4!+3!-2!+1!$$
  17. $$18!-17!+16!+15!+14!-13!-12!+11!+10!+9!+8!-7!+6!-5!+4!+3!-2!+1!$$
  18. $$19!+18!+17!+16!+15!+14!+13!+12!+11!+10!+9!+8!+7!+6!+5!+4!+3!+2!-1!$$
  19. $$20!-19!+18!+17!+16!+15!+14!+13!+12!+11!+10!+9!+8!+7!+6!+5!+4!+3!+2!-1!$$
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