Thanks to a query of A. Venkatesh, I have just been looking at the tangled and instructive etymology of the word sieve…
To the Greeks, a sieve is a koskinon (κóσκινον), whether it be of use as a cooking utensil, or as devised by that clever fellow, Eratosthenes, to find prime numbers. But the English word has a completely different etymology, of Germanic origin if the OED is to be believed.
From the same source, I’ve learnt that a coarse-meshed sieve can also properly be called a ridder or a riddle (the latter being an alteration of the former). In this form, it is said to be related to the Indo-European stem kreit-, which is also, as it turns out, (carrying a meaning of to separate, to judge) at the root of many fine words, such as crisis, critic, criterion; through the Latin cribrum, it leads to the French word for sieve, namely crible. (Though, as far as cooking is concerned, the instrument is rather called a tamis in French cuisine; this last word, although considered obsolete, does exist in English, as does the variant temse…)
As for the Greek word, it has left no trace in French, and (apparently) remains in English only under the guise of a delightful word, coscinomancy, which I regret not having known about at the time of deciding on the title of my inaugural lecture:
< medieval Latin coscinomantia, < Greek κοσκινόμαντις, < κόσκινον sieve.
Divination by the turning of a sieve (held on a pair of shears, etc.).
1603 C. HEYDON Def. Iudiciall Astrol. xvii. 356 Comparing Astrologie with Aruspicie, Hydromancie, Chiromancie, Choschinomancie, and such like.
1653 H. MORE Antidote Atheism (1712) III. ii. 89 Coskinomancy, or finding who stole or spoiled this or that thing by the Sieve and Shears.
1777 J. BRAND Observ. Pop. Antiq. (1870) III. 301–2.
1871 E. B. TYLOR Primitive Culture I. 116 The so-called coscinomancy, or, as it is described in Hudibras, ‘th' oracle of sieve and shears’.
(To quote the OED again; note the amusing oscillations of the popularity of this word…)