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Bairstow had only returned to the UK just few days before the beginning of the series after spending eight weeks with Punjab Kings in the IPL 2022, blasting the white ball to all corners.
The second Test between England and New Zealand was won by England by 5 wickets at Trent Bridge on Tuesday, making it one of the most historic test cricket matches ever played.
With a match-winning century against New Zealand, the 31-year-old batsman became just England's second batsman to surpass 10,000 Test runs.
Jofra Archer became the third England bowler to be ruled out for the summer with a stress fracture, following Saqib Mahmood and Matthew Fisher.
Joe Root and Alastair Cook were exactly the same age when they reached the milestone - 31 years and 157 days.