On démontre que l’intervalle contient un entier ayant au plus deux facteurs premiers dès que est un nombre réel suffisamment grand.
For any sufficiently large real number , the interval contains at least one integer having at most two prime factors .
@article{AIF_1981__31_4_37_0, author = {Iwaniec, Henryk and Laborde, M.}, title = {$P\_2$ in short intervals}, journal = {Annales de l'Institut Fourier}, volume = {31}, year = {1981}, pages = {37-56}, doi = {10.5802/aif.848}, mrnumber = {83e:10061}, zbl = {0472.10048}, language = {en}, url = {http://dml.mathdoc.fr/item/AIF_1981__31_4_37_0} }
Iwaniec, Henryk; Laborde, M. $P_2$ in short intervals. Annales de l'Institut Fourier, Tome 31 (1981) pp. 37-56. doi : 10.5802/aif.848. http://gdmltest.u-ga.fr/item/AIF_1981__31_4_37_0/
[1] Combinatorial strengthening of the sieve method of Eratosthenes (Russian), Uspehi Math. Nauk., 22 (1967), n° 3 (135), 199-226. | Zbl 0199.09001
,[2] On the distribution of almost primes in an interval, Scientia Sinica, 18 (1975), 611-627. | MR 56 #15584 | Zbl 0381.10033
,[3] On the distribution of almost primes in an interval (II), Scientia Sinica, 22 (1979), 253-275. | MR 82d:10065 | Zbl 0408.10030
,[4] Sieve Methods, London 1974. | MR 54 #12689 | Zbl 0298.10026
and ,[5] Almost-primes in short intervals, to appear. | Zbl 0461.10041
, and ,[6] A new form of the error term in the linear sieve, Acta Arith., 27 (1980), 307-320. | MR 82d:10069 | Zbl 0444.10038
,[7] An improvement of Selberg sieve method, I, Acta Arith., 11 (1965), 217-240. | MR 34 #2540 | Zbl 0128.26902
and ,[8] Les sommes trigonométriques de Chen et les poids de Buchstab en théorie du crible, Thèse de 3e cycle, Université de Paris-Sud.
,[9] Buchstab's sifting weights, Mathematika, 26 (1979), 250-257. | MR 82m:10070 | Zbl 0429.10028
,[10] Van der Corput's method and the theory of exponent pairs, Quart. J. Oxford, (2) 6 (1955), 147-153. | MR 17,240a | Zbl 0065.27802
,[11] Selberg's sieve with weights, Mathematika, 16 (1969), 1-22. | MR 40 #119 | Zbl 0192.39703
,[12] The theory of the Riemann Zeta-Function, Oxford 1951. | MR 13,741c | Zbl 0042.07901
,