Primality proof for n = 6739986666787659948666753771754907668409286105635143120275902562187:

Take b = 2.

b^(n-1) mod n = 1.

123513195593586463868249598285337146648031981 is prime.
b^((n-1)/123513195593586463868249598285337146648031981)-1 mod n = 3684855820504144349110163561753049550411353570460994066703228181087, which is a unit, inverse 2914542525993049950351669929976071150836144637470163475747802315325.

(123513195593586463868249598285337146648031981) divides n-1.

(123513195593586463868249598285337146648031981)^2 > n.

n is prime by Pocklington's theorem.