Prime Numbers and the Riemann Hypothesis

1. Thoughts about numbers, 2. What are prime numbers?, 3. 'Named' prime numbers, 4. Sieves, 5. Questions about primes, 6. Further questions about primes, 7. How many primes are there?, 8. Prime numbers viewed from a distance, 9. Pure and applied mathematics, 10. A probabilistic 'first' guess, 11. What is a 'good approximation'?, 12. Square root error and random walks, 13. What is Riemann's hypothesis?, 14. The mystery moves to the error term, 15. Césaro smoothing, 16. A view of Li(X) - pi(X), 17. The prime number theorem, 18. The staircase of primes, 19. Tinkering with the staircase of primes, 20. Computer music files and prime numbers, 21. The word 'spectrum', 22. Spectra and trigonometric sums, 23. The spectrum and the staircase of primes, 24. To our readers of part I, 25. Slopes and graphs that have no slopes, 26. Distributions, 27. Fourier transforms: second visit, 28. Fourier transform of delta, 29. Trigonometric series, 30. A sneak preview, 31. On losing no information, 32. Going from the primes to the Riemann spectrum, 33. How many thi's are there?, 34. Further questions about the Riemann spectrum, 35. Going from the Riemann spectrum to the primes, 36. Building pi(X) knowing the spectrum, 37. As Riemann envisioned it, 38. Companions to the zeta function.... Mehr