I would assume that they would need industrial size centrifuges to procees nuke material. That number seems unbelievable to me. I wonder how many we have in the US? I bet not that many. Of course if they counted medical centrifuges like your hospital or dentist has, then 4000 might be believable. It just sounds to me like the gross exaggeration that might come from a place like North Korea.
There are technologies for small centrifuges:
Gas Centrifuge Uranium Enrichment
http://www.globalsecurity.org/wmd/intro/u-centrifuge.htm
A single centrifuge might produce about 30 grams of HEU per year, about the equivalent of five Separative Work Unit (SWU). As as a general rule of thumb, a cascade of 850 to 1,000 centrifuges, each 1.5 meters long, operating continuously at 400 m/sec, would be able to produce about 20-25 kilograms of HEU in a year, enough for one weapon. One such bomb would require about 6,000 SWU.