Mathematics Tripos Papers

  • Part IA
  • Part IB
  • Part II
  • FAQ

Paper 2, Section I, F

Number Theory | Part II, 2014

Show that

∑p⩽x1p⩾log⁡log⁡x−12\sum_{p \leqslant x} \frac{1}{p} \geqslant \log \log x-\frac{1}{2}p⩽x∑​p1​⩾loglogx−21​

Deduce that there are infinitely many primes.

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