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AIME I Algebra Arithmetic Math Olympiad USA Math Olympiad

Smallest prime Problem | AIME I, 1999 | Question 1

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1999 based on Smallest prime.

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1999 based on Smallest prime and arithmetic sequence.

Smallest prime Problem – AIME I, 1999


Find the smallest prime that is the fifth term of an increasing arithmetic sequence all four preceeding terms also being prime.

  • is 107
  • is 29
  • is 840
  • cannot be determined from the given information

Key Concepts


Smallest prime

Arithmetic Sequence

Algebra

Check the Answer


Answer: is 29.

AIME I, 1999, Question 1

Elementary Number Theory by David Burton

Try with Hints


Let the sequence be p, p+a, p+2a, p+3a, p+4a where p is prime and a is positive integer here p cannot be multiple of 2 or 3 or 4

then smallest p=5 taking a=6 we get a sequence of prime numbers

5,11,17,23,29 then fifth term =29.

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