SYMmetryplus75

Number 75 Summer 2021 HANDS ON POLYHEDRA These polyhedra were seen earlier this year, after lockdown allowed more local travel. The two striking yellow and blue creations, named The Nursling Murmurings, are the work of artist Martin Heron who worked with three local schools featuring their handprints and the murmurations of birds. The faces consist of octagons, hexagons, squares and rhombi. The central dodecahedron was spotted in a playground at Milton-on-Sea and the projections on the side allows children to climb to the top. Digitally delicate primes Digitally delicate primes are prime numbers that become composite numbers if you change any one of their digits to any other digit. The smallest example of this is 294001 . This means that any variation of this number, such as 894001 (= 587 × 1523) , 204001(= 7 × 151 × 193) or 294061(= 157 × 1873) , are not prime. There are infinitely many such numbers! The first few are 294001 , 505447 , 584141 , 604171 , 971767 , 1062599 , … You can find more at https://oeis.org/A050249 . These are relatively new discoveries, as in 1978 Murray Klamkin wondered if any such numbers like this existed and Paul Erdős proved that there is an infinite number of them. In 2011 Terrance Tao, a Fields Medal winner, proved that a ‘positive proportion’ are digitally delicate – this means the difference between consecutive digitally delicate primes remains fairly steady as the primes get really big, i.e., they do not become more and more scarce. Recently Michael Filaseta and Jeremiah Southwick found that if you include an infinite number of leading zeroes, then such ‘widely digitally delicate primes’ do exist though they could not find one in searching all the integers up to 1000000 . So, there’s a challenge for you! Recent News