How Long Can Sperm Stay In The Body Before Fertilizing?

Hi. I need to know as a fact if it s possible, and if I don t need to worry for a pregnancy that seems to be 2 weeks off. Her last period was on dec 3 and she was ovulating 16-17 dec. After 4 med consults the fetus is only 6 weeks today. Doctor said something like microarrays. What s hard is, we did an ovulating test to know with precision... And we only had sex twice that month and never again. Should I do a paternity test? If I am not mistaken sperm cannot last much more than 7 days in special conditions and I am very skeptic of just saying: it s magic! Or a miracle