Programme 3: Prime Numbers Think of a number. Any number. Chances are you haven't plumped for 213,466,917 -1. To get this, you would need to keep multiplying 2 by itself 13,466,917 times, and then subtract 1 from the result. When written down it's 4,053,900 digits long and fills 2 telephone directories. So, as you can imagine, it's not the kind of number you're likely to stumble over often. Unless you're Bill Gates checking your bank statement at the end of the month.

Programme 4: Kepler's Conjecture Sir Walter Raleigh was a poet, adventurer and all-round Elizabethan scallywag. In between searching for El Dorado and harrying the Spanish fleet, he is credited with introducing the humble potato to England. He was also the first Brit to seriously go over their Duty Free tobacco allowance on his return from the Americas. One of his more obscure contributions to posterity however, lies in mathematics. Raleigh wanted to know if there was a quick way of estimating the number of cannonballs in a pile.

Programme 5: Game Theory Not long ago auctions seemed to be the preserve of either the mega-rich, bidding for Van Goghs at some plush auction house, or the shady car-dealer, paying cash-no-questions-asked for vehicles of dubious provenance. However, the advent of the Internet and David Dickinson has changed this. Auction web-sites allow the average punter to buy and sell pretty much anything, whilst an army of Bargain Hunt devotees can now happily tell their Delft from their Dresden.

Professor of Genetics Steve Jones challenges evolutionary psychology, the controversial new science of how our brains and minds developed.

Professor of Genetics Steve Jones challenges the controversial science of evolutionary psychology. Evolutionary psychologists say human behaviour, such as who we marry, when we have children and even the quality of our sex lives, can be explained by having a Stone Age brain in a 21st century body. Professor Jones examines the scientific evidence for such claims and asks if we should be worried if contentious theories escape the world of science and enter the arena of social policy.

In 1996 US entrepreneur and explorer Gary Comer took his boat to the Northwest Passage in search of adventure. Inspired by the stories of early explorers like Roald Amundsen, who had tried to navigate the winding route through northern Canadian sea ice, Comer expected high adventure. Instead he found where there had once been ice, there was now easily navigated open water.

In October 1945, the magazine Wireless World published an article by a relatively unknown writer and rocket enthusiast. Its title was: "Extra-Terrestrial Relays: Can Rocket Stations Give World Wide Radio Coverage?" Today, the author's name is known throughout the world. He is the science fiction writer Arthur C Clarke, and his prediction of satellite communications has come true in ways even he never imagined. Heather Couper travels to Sir Arthur's home in Sri Lanka to hear his own story.

Life is all about the choices we make. But what happens when you’re trapped in the headlights of indecision? A light-hearted programme for ditherers who want to become decisive.

Life is all about the choices we make. But what happens when you’re trapped in the headlights of indecision? A light-hearted programme for ditherers who want to become decisive.

Penny Marshall tells the story of how the battle for birth has been waged between women, doctors and midwives over the last two centuries. This war has shaped the maternity services in the UK today. Penny talks to midwives, obstetricians, mothers and policy makers about the battles that have been fought to give women the maternity care they want.

Arcade Fire are that rare combination of things - a popular, critically-acclaimed Canadian band. As they release their third album and gear up to headline the Reading and Leeds Festival, Radio 1 heads to Montreal to spend time with frontman Win Butler and his troupe of multi-instrumentalists.

Scientist and broadcaster Prof Trevor Cox explores a new wave of biomimicry - copying nature - which aims to recreate the processes and systems, from self-cleaning lotus leaves to the Namibian fog-basking beetle, which can harvest moisture from the dry desert air. Trevor meets the people attempting to emulate nature's genius. Their goal is not just to copy nature's structures, but to recreate the processes and systems that evolution has taken billions of years to perfect.

With drama and flair, novelist Keneally illuminates the birth of New South Wales in 1788, richly evoking the social conditions in London, miserable sea voyage and the desperate conditions of the new colony. His tale revolves around Arthur Phillips, the ambitious captain in the Royal Navy who would become the first governor of New South Wales

This is the story of a remarkable friendship between a reclusive writer and illustrator ('a middle class scum ponce, if you want to be honest about it, Alexander) and a chaotic, knife-wielding beggar whom he gets to know during a campaign to release two charity workers from prison.

A gripping story of a child’s journey through hell and back. There may be as many as 300,000 child soldiers, hopped-up on drugs and wielding AK-47s, in more than fifty conflicts around the world. Ishmael Beah used to be one of them. He is one of the first to tell his story in his own words. In this book, Beah, tells a riveting story. At the age of twelve, he fled attacking rebels and wandered a land rendered unrecognizable by violence. By thirteen, he’d been picked up by the government army, and Beah, at heart a gentle boy, found that he was capable of truly terrible acts.

Published to coincide with the thirty-fifth anniversary of Jimi Hendrix's death, Room Full of Mirrors gives full voice to the music that continues to enthrall each successive generation of rock fans. Hendrix's colorful, tumultuous life is brilliantly detailed in Charles Cross's latest rock bio

Nick Thorpe takes the reader on boat-hopping odyssey through Scotland's canals, lochs and coastal waters, from the industrial Clyde to the scattered islands of Viking Shetland. Whether rowing a coracle with a chapter of monks, scanning for the elusive Nessie, hitting the rocks with Captain Calamity or clinging to the rigging of a tall ship, Thorpe weaves a narrative that is by turns funny and poignant - a nautical pilgrimage for any who have ever been tempted to try a new path just to see where it might take them. Part travelogue, part memoir, Adrift in Caledonia is a unique portrait of a sea-fringed nation

Chapman, a criminal, sybarite and serial philanderer, found himself on Jersey when the Germans invaded and was transferred to a hellhole of a prison in Paris. The only way out of this benighted existence was to volunteer his services to the Abwehr as a secret agent. Eventually accepted, he was then parachuted into England, where he promptly landed flat on his face and then swiftly handed himself over to the police and volunteered to become a secret agent

Alistair Cooke, then a Washington correspondent for "The Guardian," recognised a great story to be told in investigating at first hand the effects of the Second World War on America and the daily lives of Americans as they adjusted to radically new circumstances. Within weeks of the Pearl Harbor attack, with a reporter's zeal, Cooke set off on a circuit of the entire country to see what the war had done to people. This unique travelogue celebrates an important American character and the indomitable spirit of a nation that was to inspire Cooke's reports and broadcasts for some sixty years

William Boyd's first collection of non-fiction is a substantial volume of writings from the last three decades that range widely over his particular interests and obsessions. Bamboo gathers together Boyd's writing on literature, art, the movie business, television, people he has met, places he has visited and autobiographical reflections on his African childhood, his years at boarding school and the profession of novelist. From Pablo Picasso to the allure of the British Caff, from Charles Dickens to Catherine Deneuve, from mini-cabs to Brideshead Revisited, this collection proves a fascinating and surprisingly revealing companion to the work of one of Britain's leading novelists.

It’s 1974 and young Rory is about to enter his second year at Cambridge, absolutely determined to have a meaningful relationship with a woman, or at least, lose his virginity

Beatrix Potter, the twentieth century's most beloved children's writer and illustrator, created books that will forever conjure nature for millions. Yet though she is a household name around the world, her personal life and her other significant achievements remain largely unknown. This remarkable new biography is a voyage of discovery into the story of an extraordinary woman. At a time when plunder was more popular than preservation, she brought nature back into the English imagination. "Beatrix Potter: A Life In Nature" reveals a strong, humorous and independent woman, whose art was timeless, and whose generosity left an indelible imprint on the countryside.

David Profumo was just seven when his father, who had been Secretary of State for War, resigned from the Macmillan government. Despite the furore and humiliation that followed, his parents famously stayed together -- and now, forty years on, their son has written this long-awaited account of their family life before, during and after the sensational events of 1963.

This singular tale by Whitbread Prize-winning writer Diana Souhami ('Selkirk's Island') connects the famous mutiny on the Bounty in the Pacific Ocean in 1789 to the plight of the islanders of Pitcairn now. Its conceptual core is how a small chance thing, the taking of a coconut by Fletcher Christian from William Bligh's stores on the ship, had dramatic ramifications that continue today.

Michael Palin has kept a diary since newly married in the late 1960s, when he was beginning to make a name for himself as a TV scriptwriter (for the Two Ronnies, David Frost etc). Monty Python was just around the corner. This first volume of his diaries reveals how Python emerged and triumphed, how he, John Cleese, Graham Chapman, the two Terrys - Jones and Gilliam - and Eric Idle, came together and changed the face of British comedy.

A dramatic, sparkling tale of sex, glamour, intrigue, romance and heartbreak, "England's Mistress" traces the rise and rise of the gorgeous Emma Hamilton. Born into poverty, she clawed her way up through London's underworlds of sex for sale to become England's first media superstar.

This evocation of a way of life now vanished demonstrates the power of the word to make the local universal and to bring the past timelessly to life. Woven into the fabric of family life, village characters, church and school, Rush writes of folklore and fishing and the eternal power of the sea, the cycle of the seasons, the worlds of the imagination and the unknown, the archetypal problems of fathers and sons and mother love, and the inescapability of childhood influences far on into adult life.

In 1945, a small-time Dutch art dealer was arrested for selling a forgery of a priceless national treasure - a painting by Vermeer - to Hitler's right-hand man. The charge was treason, the only possible sentence death. And yet Han van Meegeren languished in his dank prison cell, incapable of uttering the words that would set him free: 'I am a forger.' This riveting account of greed, hubris, excess, treason and fine art is the story of a failed artist and the greatest forger of all time, who executed a swindle which earned him the equivalent of fifty million dollars and the acclaim of the very critics who had mocked him.

Samuel Sewall sat in judgement at the Salem witch trials. Five years later he recanted the guilty verdicts. Through his story, Richard Francis brings the New World vividly to life. The Salem witch trials of 1692 have assumed mythical status. Immortalised by Arthur Miller's The Crucible, the witch-hunt is now part of our vocabulary. Yet the actual events are more remote than ever. Biographer and novelist Richard Francis brings the reality back into focus with the story of Samuel Sewall, New England Puritan, Salem trial judge, publisher, entrepreneur and writer.

The definitive biography of Leni Riefenstahl, the woman best known as "Hitler's filmmaker," one of the most fascinating and controversial personalities of the twentieth century. It is the story of huge talent and huger ambition, one that probes the sometimes blurred borders dividing art and beauty from truth and humanity