78,557 MathCityMap Tasks!
The MathCityMap web portal recently added 78,557 tasks. Within a few weeks, almost 3 thousand tasks have been added and it is likely that the 80,000 tasks will be cracked just as quickly in the near future. We are very proud and particularly pleased about the many dedicated community members who regularly create exciting tasks for their learners to offer them added value and a change from regular math lessons.
What’s the story behind the number 78,557? It is the smallest Sierpinski number found to date. Larger numbers have also been found, but none smaller so far. The question of whether this is the smallest Sierpinski number has been unanswered since 1967. The second project is currently underway to check whether there is another smaller number in the number set for which the conditions apply1.
A Sierpinski number k is an odd natural number for which it is true that no prime number appears anywhere in the set {k⋅2n+1 : n ∈ IN}2 The US mathematician John L. Selfridge proved that 78,557 is a Sierpinski number by first showing that 78,557⋅2n+1 is divisible by at least one of the primes {3, 5, 7, 13, 19, 37, 73} for all n greater than or equal to 1. He then established that this is repeated every 36n in a so-called covering set. All cases can then be covered by congruence3.
We are already looking forward to reaching 80,000 tasks and many other milestones.
