Davies is running a further 18 laps to reach the 5,000km mark and will become the first Kiwi to do so.
Only one other Kiwi has attempted and finished the race. In 2010, Aucklander Dharbhasana Lynn, 34, became the first New Zealander to finish the race. Davies' feat makes it only two Kiwis who have done so.
"It seems pretty definite from the way the last 50 days have gone that I'll finish and yet every lap is a miracle ... I'm praying that nothing goes wrong," Davies said during the 51st day.
"Some days overall are a little easier than others, but most days are pretty tough in many different ways. Physically, or mentally, or emotionally and so I don't think it gets easier.
"In a way having the finish line coming closer is challenging because you keep thinking of finishing and yet every lap is full of new surprises or new challenges."
Day 27... from Perfection Journey Films on Vimeo.
1
Labelled by the New York Times "the Mount Everest of Ultramarathons", the annual event in its 21st year begins at 6am and finishes at 12am.
Participants can choose whether to take breaks along the way or how far they run each day but it must be completed within 52 days, an average of 96km per day - just over two marathons.
Russian man Vasu Duzhiy 51, of St Petersburg, Russia, won this year's race, finishing in 46 days. Second - and first woman - was Kaneenika Janakova,47, of Bratislava, Slovakia, who set a new women's world record for the distance. Her final time was 48 days.
And third place was Nirbhasa Magee, a native of Dublin, Ireland, who also finished in 48 days.
