A295262 Primes for "Landau's trick" to prove Bertrand's postulate for n < 4000.

2, 3, 5, 7, 13, 23, 43, 83, 163, 317, 631, 1259, 2503, 4001

Offset

1,1

Comments

Chapter 2 in the Aigner and Ziegler book is devoted to Bertrand's postulate. The proof given starts by showing Bertrand's postulate is true just for n < 4000.

After 2, each prime is less than twice the previous prime. So, even if these were the only primes up to 4002, Bertrand's postulate would still be true for the specified range.

However, these are different from the Bertrand primes (A006992) after 2503, as that sequence requires the very largest prime smaller than twice the previous one, since twice 2503 is 5006 and 5003 is the largest prime less than that.

Erdős Pál used this sequence, with 4001 instead of 5003, in his 1932 proof of Bertrand's postulate, attributing it to Edmund Landau ("einer Bemerkung des Herrn Landau"), which Aigner and Ziegler refer to as "Landau's trick" in their book.

References

Martin Aigner and Günter M. Ziegler, Proofs from the Book, Second Edition. Berlin (2001): Springer-Verlag, p. 7.

Links

Table of n, a(n) for n=1..14.

Erdos Pál, Beweis eines Satzes von Tschebyshef, Acta Sci. Math (Szeged) 5 (1930-1932), p. 198 (in German).

Crossrefs

Cf. A006992.

Sequence in context: A235394 A126092 A132394 * A006992 A185231 A080190

Adjacent sequences: A295259 A295260 A295261 * A295263 A295264 A295265

Keyword

nonn,fini

Author

Alonso del Arte, Nov 18 2017

Status

approved