Mathematics
It is the tenth prime number, and also the fourth primorial prime. It forms a twin prime pair with thirty-one, which is also a primorial prime. Twenty-nine is also the sixth Sophie Germain prime. It is also the sum of three consecutive squares, 22 + 32 + 42. It is a Lucas prime, a Pell prime, and a tetranacci number. It is an Eisenstein prime with no imaginary part and real part of the form . Since 18! + 1 is a multiple of 29 but 29 is not one more than a multiple 18, 29 is a Pillai prime. 29 is also the 10th supersingular prime.
None of the first 29 natural numbers have more than two different prime factors. This is the longest such consecutive sequence.
29 is the aliquot sum of the odd discrete biprimes 115 and 187 and is the base of the 29-aliquot tree.
29 is a Markov number, appearing in the solutions to : {2, 5, 29}, {2, 29, 169}, {5, 29, 433}, {29, 169, 14701}, etc.
29 is a Perrin number, preceded in the sequence by 12, 17, 22.
Since the greatest prime factor of 292 + 1 = 842 is 421, which is obviously more than 29 twice, 29 is a Størmer number.
Read more about this topic: 29 (number)
Famous quotes containing the word mathematics:
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—Walter Reisch (1903–1963)
“Mathematics alone make us feel the limits of our intelligence. For we can always suppose in the case of an experiment that it is inexplicable because we don’t happen to have all the data. In mathematics we have all the data ... and yet we don’t understand. We always come back to the contemplation of our human wretchedness. What force is in relation to our will, the impenetrable opacity of mathematics is in relation to our intelligence.”
—Simone Weil (1909–1943)
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—Willard Van Orman Quine (b. 1908)