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I disagree with this. The active prosthetic group is a complex of molybdpterin and a metal, either molybdenum or tungsten. Molybdopterin itself and molybdopterin nucleotides do not (contrary to what the name suggests) contain molybdenum. It is a bit of misnomer, which can lead to confusing terminology such as bis(molybdopterin)tungsten cofactor (CHEBI:30402). So the alternative nomenclature was proposed that uses term "pyranopterin" but it was slow to be accepted.

See also classification in http://www.ebi.ac.uk/come/entry?gn=PRX000011

Currently in ChEBI

bis(molybdopterin guanine dinucleotide)molybdenum (CHEBI:22894) is a molybdopterin cofactor (CHEBI:25372)
bis(molybdopterin)tungsten cofactor (CHEBI:30402) is a molybdopterin cofactor (CHEBI:25372)
molybdenum cofactor (CHEBI:21437) is a molybdopterin cofactor (CHEBI:25372)

I think these are correct. However

L-cysteinyl molybdopterins (CHEBI:21275) is a molybdopterin cofactor (CHEBI:25372) CHECKED
L-selenocysteinyl molybdopterin guanine dinucleotide (CHEBI:21386) is a molybdopterin cofactor (CHEBI:25372)
L-serinyl molybdopterin guanine dinucleotide (CHEBI:21392) is a molybdopterin cofactor (CHEBI:25372)

these relationships are wrong and I will delete them. Cys, Ser and Sec are residues of corresponding enzymes which coordinate to metal of the cofactor but should not be considered as cofactor itself.