By Paul Lewis
BBC Radio 4's Money Box
The government has rejected claims that 500,000 women may have been underpaid state pensions by £1bn a year.
Some women may have missed out on their full entitlement
They were made by Liberal Democrat head of policy Steve Webb MP and The Times newspaper.
They said government computers had not always put the correct note on their National Insurance record when they left work to have children.
But Pensions Minister James Purnell said the story was "completely wrong" and that "very few" would be affected.
Speaking to BBC Radio 4's Money Box programme Mr Purnell called The Times "irresponsible" for publishing the figures before he had been able to check them.
But Steve Webb defended the calculation: "We've done some quite detailed sums based on parliamentary questions.
"Accountants Grant Thornton have looked at them and think the assumptions are quite conservative. It is an estimate."
The Times interviewed 64-year-old Kay Rumble from Berkshire who had taken time off work to look after her three children.
Her state pension was just £25.23. But when she complained and pointed out that she had been getting child benefit for some years it was revised up by nearly £20 a week to £45.12.
Steve Webb explained what had gone wrong. "The typical scenario is a child born in the late 1960s or 70s. "The mother stops work, perhaps only pays the married woman's NI contribution but after a few years out of work she should have been getting this protection.
"We don't think there was any automatic way that they got their Home Responsibilities Protection."
Steve Webb said such problems were widespread and that women who claimed Child Benefit did not have the fact automatically noted on their National Insurance record.
"We don't think that government computers in the 1980s in different departments were talking to each other. There is strong evidence that the government needs to find these women."
James Purnell disagreed.
"Where Steve says they might have been a mistake in the system and people slipped through the gap, in both cases there were fail-safe systems so they were caught in another way," he said.
He conceded there would be some individual cases but added: "We are confident they are very few. The allegation that these cases weren't being checked in the 1970s is wrong.
"When people didn't put their NI number on their child benefit form it was reconciled clerically."
Any woman who has claimed child benefit in the past and now has a reduced state pension can get it checked by calling the Pension Service on 0845 3000 168 and asking it to check that she has been given the correct Home Responsibilities Protection in her pension calculation.
BBC Radio 4's Money Box was broadcast on Saturday, 12 May 2007 at 1204 BST.
The programme was repeated on Sunday, 13 May 2007 at 2102 BST.