In 1965 Erdős introduced : is the smallest integer such that every is the sum of s distinct primes or squares of primes where a prime and its square are not both used. We prove that for all sufficiently large s, , and the set of s with the equality has the density 1.
En 1965 Paul Erdős a introduit la valeur comme le plus petit entier tel que tout entier est la somme de s premiers ou carrés de premiers distincts, où un nombre premier et son carré ne sont simultanément utilisés. Nous démontrons que pour tout s suffisamment grand on a et que lʼensemble des s réalisant lʼégalité est de densité 1.
Accepted:
Published online:
@article{CRMATH_2012__350_13-14_647_0, author = {Fang, Jin-Hui and Chen, Yong-Gao}, title = {On the sum of distinct primes or squares of primes}, journal = {Comptes Rendus. Math\'ematique}, pages = {647--649}, publisher = {Elsevier}, volume = {350}, number = {13-14}, year = {2012}, doi = {10.1016/j.crma.2012.08.003}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2012.08.003/} }
TY - JOUR AU - Fang, Jin-Hui AU - Chen, Yong-Gao TI - On the sum of distinct primes or squares of primes JO - Comptes Rendus. Mathématique PY - 2012 SP - 647 EP - 649 VL - 350 IS - 13-14 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2012.08.003/ DO - 10.1016/j.crma.2012.08.003 LA - en ID - CRMATH_2012__350_13-14_647_0 ER -
%0 Journal Article %A Fang, Jin-Hui %A Chen, Yong-Gao %T On the sum of distinct primes or squares of primes %J Comptes Rendus. Mathématique %D 2012 %P 647-649 %V 350 %N 13-14 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2012.08.003/ %R 10.1016/j.crma.2012.08.003 %G en %F CRMATH_2012__350_13-14_647_0
Fang, Jin-Hui; Chen, Yong-Gao. On the sum of distinct primes or squares of primes. Comptes Rendus. Mathématique, Volume 350 (2012) no. 13-14, pp. 647-649. doi : 10.1016/j.crma.2012.08.003. http://archive.numdam.org/articles/10.1016/j.crma.2012.08.003/
[1] V. Brun, Le crible dʼEratosthene et le théorème de Goldbach, Videnskapselkapets Skrifter, I, No. 3, Kristiania, 1920.
[2] The analogue of Erdős–Turán conjecture in , J. Number Theory, Volume 128 (2008), pp. 2573-2581
[3] On a problem of Sierpiński, Acta Arith., Volume 11 (1965), pp. 189-192
[4] Sur les suites dʼentiers deux á deux premiers entre eux, Enseign. Math., Volume 10 (1964), pp. 229-235
Cited by Sources:
☆ This work was supported by the National Natural Science Foundation of China, Grant Nos. 11071121, 11201237 and the Youth Foundation of Mathematical Tianyuan of China, Grant No. 11126302. The first author is also supported by the Natural Science Foundation of the Jiangsu Higher Education Institutions, Grant No. 11KJB110006.