{"version":9,"randomSeed":"5ac4bab58ccbd86e987a650a5f0cf292","graph":{"viewport":{"xmin":-1.8188303069058243,"ymin":-1.134930834958654,"xmax":26.515488887217682,"ymax":15.024705842868913},"squareAxes":false},"expressions":{"list":[{"type":"text","id":"15","text":"OEIS A000110, \"Bell exponential numbers\" https://oeis.org/A000110"},{"id":"12","type":"table","columns":[{"values":["","1","2","3","4","5","6","7","8","9","10","11","12","13","14","15","16","17","18","19","20"],"hidden":true,"id":"10","color":"#000000","latex":"x_{1}"},{"values":["","1","2","5","15","52","203","877","4140","21147","115975","678570","4213597","27644437","190899322","1382958545","10480142147","82864869804","682076806159","5832742205057","51724158235372"],"id":"11","color":"#c74440","latex":"y_{1}"}]},{"type":"text","id":"17","text":"Define a Bell pseudoprime to be a composite number n such that a(n) == 2 (mod n). W. F. Lunnon recently found the Bell pseudoprimes 21361 = 41*521 and C46 = 3*23*16218646893090134590535390526854205539989357 and conjectured that Bell pseudoprimes are extremely scarce. So the second Bell pseudoprime is unlikely to be known with certainty in the near future. I confirmed that 21361 is the first. - David W. Wilson, Aug 04 2007 and Sep 24 2007"},{"type":"expression","id":"21","color":"#2d70b3","latex":"B\\left(n\\right)=\\sum_{k=1}^{2n}\\operatorname{mod}\\left(\\frac{k^{n}}{e\\left(k!\\right)},n\\right)","hidden":true},{"type":"text","id":"20","text":"therefore, if mod(Bell(n), n) == 2, n is probably prime (but this test does not say \"probably prime\" for all prime n)"},{"type":"expression","id":"25","color":"#c74440","latex":"C\\left(n\\right)=\\operatorname{mod}\\left(B\\left(n\\right),n\\right)","hidden":true},{"type":"expression","id":"18","color":"#fa7e19","latex":"0\\le y\\le1\\left\\{\\left|\\operatorname{round}\\left(C\\left(\\operatorname{round}\\left(x\\right)\\right)\\right)-2\\right|\\le0.00001\\right\\}","fillOpacity":"1"}]}}