MATHEMATICS. 



No. 105. LEHMER, DERRICK N. Factor Table for the First Ten Millions, containing 

 the smallest factor of every number not divisible by 2, 3, 5, or 7 between 

 the limits o and 10017000. Folio, xiv+476 pages. Published 1909. 



Bound in leather and buckram $20.00 



Unbound $18.00 



This table furnishes the smallest divisor of every number up to the limit 

 10017000. The multiples of 2, 3, 5, and 7 are not listed as being easily obtainable 

 from inspection. At the same time the failure to find a given number in the table 

 is evidence that it is a multiple of one of these numbers. The omission of such 

 numbers greatly reduces the bulk of the tables and adds very slightly to the com- 

 plexity of the arrangement. 



A list of smallest divisors really serves to find all of the divisors of a number, 

 for one may divide out the smallest factor as listed in the table and then proceed 

 to obtain the smallest divisor of the resulting quotient. This process may be con- 

 tinued until a quotient is obtained which is a prime. 



Factor tables for the first nine millions have already been published, but are 

 for the most part unobtainable. The tables herewith published have been com- 

 pared, entry for entry, with the previously printed tables and what is believed to 

 be a complete list of errors is also given in the Introduction. The tenth million 

 has been checked against a table in manuscript by Kulik deposited in the Vienna 

 Academy of Sciences. Comparison with all of these tables has been made five 

 times (six for the first three millions). The tables were printed by photographic 

 methods which are believed to eliminate many errors which commonly occur by 

 the falling out or breaking off of types. 



The problem of finding the factors of a given number is important in itself 

 and is constantly met with in the theory of numbers and in the theory of groups. 

 The allied problem of finding the number of primes between given limits makes 

 a reliable list of primes of the first consequence. This list can now be made as far 

 as the first ten millions, it is believed, with absolute confidence. Computations of 

 the number of primes in the successive millions, and indeed in shorter intervals, 

 tally exactly with the counts made from these tables as far as these counts have 

 been made. 



No. 165. LEHMER, DERRICK N. List of Prime Numbers from I to 10006721. Folio. 

 xvi+133 pages. Published 1914. Price $5.00. 



Until the completion of the author's Factor Table for the first ten million num- 

 bers the construction of a reliable list of primes was impossible, owing to the 

 numerous errors still undetected in the old tables of factors. The list of primes 

 herewith published is taken from the corrected tables of factors and has been 

 checked by comparison with the results of the count of primes made independently 

 of factor tables by Meissel and Bertelsen. The number of primes in each successive 

 thousand as counted by Glaisher has also been compared with the number obtained 

 from the list. The results indicate a very high degree of accuracy for the list. 



The successive primes are arranged in columns of one hundred, there being 

 fifty columns to the page. Each page thus serves to list five thousand primes. 

 The total number of pages is 133, and therefore the total number of primes listed 

 is 665,000. The page is identical in size with the page of the Factor Table. The 

 arrangement enables one to tell at a glance the rank of any particular prime and 

 the number of primes between any two given limits. 



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