However, the opportunity may not be as good as it looks.
More than 21 million people already hold the bonds, which are issued by Treasury-backed savings provider NS&I, and the number looks likely to grow as a result of changes coming into effect this summer.
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From this month, the maximum amount that can be invested in Premium Bonds has risen from £30,000 to £40,000, giving holders an improved chance of winning tax-free cash in the monthly prize draws. A further increase to £50,000 is planned for next spring.
And from August, Ernie - the Blackpool-based random number generator that chooses the winners - will create not just one but two new millionaires every month, doubling every holder's chance of hitting the jackpot, no matter what size their stake.
Julian Hynd, NS&I's retail director, said: "Raising the maximum amount that can be invested is good news for customers, because the more they invest, the greater their chance of winning a tax-free prize.
"I'm sure many of the 600,000 customers who currently have the maximum holding of £30,000 will want to invest more."
The last time the investment limit went up was in May 2003, when it increased from £20,000 to £30,000. Since then, the total amount invested has risen from £19.7 billion to £45.7 billion.
Bonds, which cost £1 each, earn no interest but they are entered into the monthly draw for prizes of £25 upwards. Holders' money is fully protected by the Treasury's guarantee and can be withdrawn at any time without penalty.
Over the course of a year, prizes are worth 1.3 per cent of the total invested.
But that doesn't mean you are guaranteed a 1.3 per cent return. Each bond has a one-in-26,000 chance of winning a prize of some kind in any given month. These odds will stay the same when the second £1 million draw is introduced, but each bond holder will have twice the chance of winning the top prize.
Winners are contacted automatically, and if they can't be reached because their details are out of date, prizes are held for them indefinitely. Holders who have lost their bond numbers or believe a dead relative may have unclaimed cash can use a special tracing service available through NS&I's website www.nsandi.com
There are currently around 900,000 unclaimed prizes totalling more than £44 million - £50,000 of this belongs to the holder of bond number 81PY499671 whose last known address was in Central Scotland.
New investors can buy bonds online, by phone on 0500 500 000, at Post Office branches, or by post from National Savings and Investments, Glasgow G58 1SB.
Mr Hynd added: "For customers who already hold Premium Bonds, they can now buy more by making a transfer from their bank account directly to us, if they wish to do so.
"Customers can also sign up to have their winnings paid directly into their account - taking away the hassle of a trip to the bank."
Because there are almost 46 billion bonds in existence, the odds on winning the million-pound jackpot in any month are currently around 46 billion to one, which will improve with a second prize - though more bonds are likely to be sold.
Anyone really serious about winning big could be better off playing the National Lottery. Although the minimum Lotto stake is £2 and non-returnable, the chances of winning a prize of some kind are approximately one in 54, while the likelihood of a ticket scooping a multi-million-pound jackpot is a mere one in 14 million.