Related papers: Explicit estimates on prime numbers

This paper has been withdrawn. (Reason) Its contents have been entirely superseded by the contents of the articles arXiv:0809.3444 and arXiv:0705.3070. There is no profitable reason to keep it alive. No material on it is however wrong.

Admin note: withdrawn by arXiv admin because of the use of a pseudonym, in violation of arXiv policy.

This paper was withdrawn by arXiv admin due to authors' misrepresentation of identity/affiliation.

This paper has been withdrawn by the authors, because it has been made obsolete by the detailed expositions in our papers in arXiv:0812.4885 (the mathematics part) and arXiv:0812.4737 (the economics part).

This paper has been withdrawn by the author due to a mistake in the proof of the main theorem.

arXiv admin comment: This version has been removed by arXiv administrators as the submitter did not have the rights to agree to the license at the time of submission

This paper has been withdrawn by the authors due to the fact that the conjecture has indeed already long been established.

Withdrawn by arXiv administration because authors have forged affiliations and acknowledgements, and have not adequately responded to charges [hep-th/9912039] of unattributed use of verbatim material.

This preprint has been withdrawn. It is because I will never publish this preprint since everything has been contained in my new preprint: arXiv:0907.1506. Please refer to arXiv:0907.1506. Please do not cite this preprint any more.

This paper has been withdrawn by the author due to an extended and largely modified version of the paper was published in arXiv (see arXiv:0807.3694, Disjoint minimal graphs).

This paper has been withdrawn by the author(s), due to the existence of a much better paper in http://arxiv.org/abs/cs.CR/0207027

This paper was withdrawn by arXiv administrators. It is an erroneous duplicate submission of math.NA/0405095.

This paper has been withdrawn by the author because Conjecture 1 is false. Please see arXiv:0901.2093 for a justification that Conjecture 1 is false. The other main results are also available from the above URL.

This submission has been withdrawn by arXiv admin. It is a verbatim copy of arXiv:0912.1810 with only the author name and title changed.

This article was withdrawn by the arXiv.org administrators since it plagiarizes math.AT/0401211.

This paper has been withdrawn by the authors due to some fatal errors in the analysis.

I give some claims on primorial prime numbers for interested readers in number theory.

arXiv admin note: This version removed by arXiv administrators as the submitter did not have the right to agree to the license at the time of submission

This submission has been withdrawn by arXiv administrators because it is intentionally incomplete, which is in violation of our policies.

This version has been removed by arXiv administrators, as we were obligated to do, due to claimed copyright infringement by a third party