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Legendre 1798 — Essai sur la théorie des nombres
chain
A.-M. Legendre (1798). Essai sur la théorie des nombres. Paris, 1798 (2nd ed. 1808). Cited by its record. License as found: public domain (the author died more than a century ago, or the work was published before 1930). What it gave the chain: the first published guess at the prime count: pi(x) is about x / (log x - 1.08366).
source
A.-M. Legendre (1798), Paris, 1798 (2nd ed. 1808)
card id
card_chain_legendre_1798
address
WIT.codex.FCT/essai-sur-la-th-orie-des-nombres/REF.WITNESSED@a-m-legendre
adjoining cards
- part of → The Riemann chain - from Euler's product and Legendre's count to the critical line — a root of this chain - one of the two trees it began from
- enables → Gauss 1849 — Letter to Encke, 24 December 1849 (the count made in 1792–93) — the logarithmic integral li(x) as the count of primes - read off the log tables he counted
- enables → Chebyshev 1852 — Mémoire sur les nombres premiers — pi(x) is between 0.92 and 1.11 times x / log x; Bertrand's postulate proven
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