384 Mr. W. Shanks on the Reciprocal [June 18, 



Given number of 



figures in Primes, Prime Factors, &c. 



Period of Primes. 



80 

 Si 



82 



83 



84 



85 



86 



8? 

 88 

 89 

 90 

 9 1 



92 

 93 



94 

 95 



96 



97 

 98 



99 



99999 91000 ooooo 99999 99100 ooooo i. 



3 6 . 163. 9397.21762 15574 17380 51978 03850 29334 29783 20758 07163 



797- 



90909 09090 90909 09090 90909 09090 90909 09091. 

 Seems prime. 



10099 98990 00099 98990 ooioi. 

 90000 90000 90000 90900 90900 90900 90909 90909 90909 90909 99909 



99909 9991. 



90909 09090 90909 09090 90909 09090 90909 09090 91. 

 4003 . 22505 64329 00549 81286 55760 43195 08116 66025 2 5583 29000 997. 

 617 . 16205 83484 60129 67584 92708 26564 02106 953. 

 Seems prime. 



29611 64229 50923 97453 00732 9. 

 547 . 14197 . 17837 . 64973 58525 58248 78623 76372 29838 67691 22282 



27693 73769 82738 03847 7. 



1289 . 76811 40495 74080 75951 11722 18851 05500 46470 9. 

 90090 09009 00900 90090 09009 00900 99099 09909 90990 99099 09909 



90991. 



6299. J 443 2 35 2 7 21211 15905 84364 04046 81839 83027 609. 

 191 . 47120 89005 70681 09952 82727 69638 69115 13141 30942 35654 



39842 88481 62827 17801. 

 97 . 10309 27835 05154 62886 59793 81443 3- 

 Seems prime. 



197.50761 41624 36553 29949 18781 72639 59390 35533. 

 199 . 397 . 12657 74717 41579 43369 23914 28173 61378 68182 22092 83191 



7775 2 7435 6 67. 

 99999 99999 ooooo oocoo 99999 99999 ooooo ooooi. 



Note. In the preparation of this paper valuable assistance was 

 received from the Eev. Prof. Salmon, F.R.S., both in the way of sugges- 

 tions and otherwise. W. S. 



Houghton -le-Sprirvg, 

 April 18, 1874. 



III. " On the Number of Figures in the Reciprocal of every 

 Prime between 20,000 and 30,000." By WILLIAM SHANKS. 

 Communicated by the Rev. GEORGE SALMON, F.R.S. Received 

 June 6, 1874. 



In a former communication* I gave the number of figures in the 

 reciprocal of every prime below 20,000 ; the present Table is simply an 

 extension of the former, and has been calculated by the same method. 

 Towards the close of the former Table, viz. opposite the prime 19841, 

 instead of 1984 read 64. The whole of the former Table has kindly been 

 verified by the Eev. Dr. Salmon. For the accuracy of the following 

 Table I am entirely responsible, and believe it is free from error. 



* Swprk, p. 200. 



