I am looking for the original article about the Cullen numbers. But all I can find is the reference to "Question 15897" in "Educ. times 534, 1905". But I cannot find the "educ times" and I can't find any information, what it is at all. Is it a journal? Can you help me with that? I found some other articles about Cullen numbers, but they all just refer to the "educ times".


4 Answers 4


This link should take you to an image of the relevant page



The Educational Times was a British journal published in the nineteenth century that addressed a wide variety of topics including a section in which readers can propose mathematical questions and submit answers to the questions that have been submitted.

See here under Info > About.

Searching for "Cullen" and going to the second results page (where we find a single entry for December 1905) gives you an entry that is probably what you are looking for:

15897 James S.J. Cullen 58 1905-12-01 James S.J. Cullen N/A N/A 85 Number Theory


(Some general information about the periodical to supplement Stephan Kolassa's answer)

Some useful information about the Educational Times can be found in Grattan-Guinness's 1992 paper A note on The Educational Times and Mathematical Questions, and in Janet Delve's 2003 paper The College of Preceptors and the Educational Times: Changes for British mathematics education in the mid-nineteenth century, and in Delve's 1999 Ph.D. thesis at Middlesex University [1]. See also the Mathematical Association of America's web page The Educational Times Database: History of the Educational Times and Mathematical Questions, 1847–1918.

The mathematics questions, sometimes with supplementary comments and additional answers (and perhaps even additional questions), were republished in Mathematical Questions and Solutions from the Educational Times.

Many of these periodical volumes can be found at the Internet Archive (Example) and at Google-Books (Example). About a year ago I spent several hours each day for a couple of weeks downloading all the volumes I could find (various google-search strategies were used; 5.6 GB of files total). In case anyone is interested, for Educational Times I was able to get 13 volumes among volumes 14-44 [2] and all of volumes 46-75. For Mathematical Questions and Solutions I managed to get every one of the volumes (75 volumes in 1st series, 29 volumes in 2nd series, 6 volumes in 3rd series).

[1] Incidentally, only the first 197 pages (and Appendix B) of Delve's thesis is online, and thus MISSING are Chapters 5, 6, 7, 8, 9 and the Bibliography -- a total of at least 168 pages. In September 2022 I informed the Middlesex library staff about this, and they eventually told me (February 2023) that apparently a mistake was made during the original digitization, and although after my inquiry they made extensive enquiries to find an original hard copy, they have been unable to locate one or to contact the author.

[2] Specifically, volumes 14, 17, 22, 23, 26, 30, 31, 33, 35, 37, 39, 42, 44.


The Educational Times.

Specifically, Volume LVIII, Dec. 1 1905, p. 534:

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