Skip to content

Please be aware that some material may contain words, descriptions or illustrations which will not reflect current scientific understanding and may be considered in today's context inaccurate, unethical, offensive or distressing.

The Royal Society: Science in the Making

Unpublished table, 'The reciprocal of every prime between 30,000 and 40,000' by William Shanks

Reference number: AP/57/4

Date: 1875

Description

Shanks shares a table of primes and their reciprocals between 30,000 and 40,000. The left-hand column of the table shows prime numbers while the right-hand column shows 'the number of figures in the period of of the reciprocal of each prime.'

Subject: Mathematics

Communicated by G [George] Salmon.

Whilst the Royal Society declined to publish this paper in full, an abstract of the paper was published in volume 23 of the Proceedings of the Royal Society as 'On the number of figures in the reciprocal of each prime number between 30,000 and 40,000'.

Reference number
AP/57/4
Earliest possible date
1875
Physical description
Ink on paper
Page extent
5 pages
Format
Manuscript

Creator name

William Shanks

View page for William Shanks

Use this record

IIIF manifest

View​ IIIF ​ manifest Opens in new tab

Open in Mirador viewer Opens in new tab

Export this record

Download PDF Opens in new tab

Citation

William Shanks, Unpublished table, 'The reciprocal of every prime between 30,000 and 40,000' by William Shanks, 1875, AP/57/4, The Royal Society Archives, London, https://makingscience.royalsociety.org/items/ap_57_4/unpublished-table-the-reciprocal-of-every-prime-between-30000-and-40000-by-william-shanks, accessed on 17 August 2026

Link to this record

https://makingscience.royalsociety.org/items/ap_57_4/unpublished-table-the-reciprocal-of-every-prime-between-30000-and-40000-by-william-shanks

Embed this record

<iframe src="https://makingscience.royalsociety.org/embed/items/ap_57_4/unpublished-table-the-reciprocal-of-every-prime-between-30000-and-40000-by-william-shanks" title="Unpublished table, 'The reciprocal of every prime between 30,000 and 40,000' by William Shanks" allow="fullscreen" frameborder="0" width="100%" height="500px"></iframe>

Hierarchy

This item is part of:

Related Fellows

Explore the collection

  • Archived Papers

    The 'Archived Papers' collection is comprised of original manuscript scientific papers and letters submitted to the Royal Society which remained unpublished or were abstracted in the journal 'Proceedings of the Royal Society' published from 1830 onwards.

    Dates: 1768 - 1989

    View collection