Paul Robson, aged 56, was reported missing from prison shortly before 7am on Sunday, February 13.
Investigating officers are urging people to call them on 999 if they have seen Robson.
Detective Chief Superintendent Andy Cox, of Lincolnshire Police, said: “We are urgently seeking the help of the public to find Robson.
“This man is a convicted rapist, serving a life sentence and is extremely dangerous.
“I believe he poses a real risk of causing significant harm to members of the community.
“Since reports of his escape came to light, we have deployed additional resources to apprehend Robson.
“He could be anywhere in the country and we are really keen to hear from the public with potential sightings so we can take this man off our streets.
“Robson is a dangerous sex offender and. while he presents a particular danger to women and young children, I believe he can cause real harm to anyone he comes across.
“If you see Robson, please do not approach him, and do not try to apprehend him yourself. Call 999 immediately.
“We are really grateful for all the shares so far and rest assured we will continue our efforts to find and arrest him.”
Robson absconded from HMP North Sea Camp, in Boston, Lincolnshire.
He is described as white, with a bald head, a long goatee beard and of slim build.
If you have seen him or have information as to where he may be, call 999.