History of Mathematics Project | Van Schooten's Prime Table

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1657

Van Schooten's Prime Table

Prime table up to 10,000

In 1657, Frans van Schooten published a table of prime numbers up to 10,000. While van Schooten's table included only a list of primes, Paul Guldin had published a table giving factors of numbers up to 10,000 (and hence implicitly listing primes in that range as numbers possessing no nontrivial factors) 16 years previously.

In 1657, Frans van Schooten published a table of primes to 10,000. The table appeared in his work Exercitationes Mathematicae, which was an early attempt to develop general methods for solving problems with numbers. Amusingly, the prime number 809 was accidentally omitted in the original Latin version, though this error was corrected in the 1659 Dutch version.

Artifact dimensions

5.9 in. × 7.6 in.

Artifact origin

Leiden, Netherlands

Timeline

Interactive Content

Computational Explanation

Van Schooten's table lists prime numbers up to 9979. The primes are arranged in 5 columns, with underscores placed under the smaller of each pair of primes that straddle multiples of 100. The table is spread across 10 pages, with each page containing primes up to consecutive multiples of 1000.

Calculating primes is straightforward using the Wolfram Language's Prime function. For example, the primes on the first page should be:

In[]:=

Prime[Range[PrimePi[1000]]]

Out[]=

{2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,293,307,311,313,317,331,337,347,349,353,359,367,373,379,383,389,397,401,409,419,421,431,433,439,443,449,457,461,463,467,479,487,491,499,503,509,521,523,541,547,557,563,569,571,577,587,593,599,601,607,613,617,619,631,641,643,647,653,659,661,673,677,683,691,701,709,719,727,733,739,743,751,757,761,769,773,787,797,809,811,821,823,827,829,839,853,857,859,863,877,881,883,887,907,911,919,929,937,941,947,953,967,971,977,983,991,997}

However, the prime number 809 was accidentally omitted in the printing process in the original Latin version (though this error was corrected in the 1659 Dutch version), so style the omitted prime in red:

redRules={809Style[809,Directive[FontFamily"Times",Red]]}

Out[]=

{809809}

Similarly, follow van Schooten in underlining the smaller of the pairs of primes that straddle a multiple of 100:

In[]:=

underlineRules=(#Style[#,Directive[FontFamily"Times",Underlined]])&/@NextPrime[Range[100,1000,100],-1]

Out[]=

{9797,199199,293293,397397,499499,599599,691691,797797,887887,997997}

(While the underscores in van Schooten's table generally appeared as underlining and so did not occupy their own rows or affect the pagination of columns, the underscores on pages 1, 4, 6, 7 and 8 sometimes take up vertical space and result in differing number counts in the various columns.)

Applying styles and formatting in columns reproduces the first page of van Schooten's table:

In[]:=

TextGridTranspose[Partition[Prime[Range[535]]/.underlineRules/.redRules/.n_Integer?(GreaterThan[997])"",35]],

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Other Resources

History of Mathematics
Cataldi's Divisor Table

History of Mathematics
Guldin's Factor Table

Additional Reading

Bullynck, M. "Factor Tables 1657–1817, with Notes on the Birth of Number Theory." Revue d'Histoire des Mathematiques, Vol. 16, No. 2, pp. 133–216, 2010.
van Schooten, F. Exercitationes Mathematicae. Leiden, Netherlands: Elsevier, pp. 394–403, 1657.
van Schooten, F. Mathematische oeffeningen, begrepen in vijf boecken. Amsterdam, Netherlands: Gerrit van Goedesbergh, 1659.

Van Schooten's Prime Table

Timeline

Interactive Content

Computational Explanation

Other Resources

History of Mathematics

History of Mathematics

Additional Reading

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