Mr Brown, 46, from Whitby, was last seen in Scarborough on May 8.
A spokesman for North Yorkshire Police said: "Peter Brown remains missing.
"Enquiries are ongoing and police are investigating all possible sightings."
Peter is described as white, 6ft 1in tall, of muscular/athletic build, unshaven, with greying brown hair.
However, police believe he may be sleeping rough so his appearance may be more dishevelled than in pictures.
He was last seen wearing a blue hoodie underneath a blue waist length jacket, loose grey cotton jogging bottoms, and blue Nike trainers.
Police believe he may be wearing a blue baseball bat and could have changed into blue jeans.
Since his disappearance there has been a huge response in the community to try and find the 46-year-old, with many people conducting searches of the area.
Posters have been up over Whitby and Scarborough and a Facebook group, 'Pete Brown Search & Updates', set up to share new information and search groups in the area, has over 3,000 members.
Natalie Brown, Peter's wife, has thanked everyone for their support and is "absolutely overwhelmed by the support of this little community."
Anyone with any information which would help police locate Mr Brown is asked to contact North Yorkshire Police on on 101 and quote reference 12190083137.