Block #680,530

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.182 × 10⁹⁷(98-digit number)

11826289817049165713…48310248232909330549

Discovered Prime Numbers

p_k = 2^k × origin − 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

origin − 1

1.182 × 10⁹⁷(98-digit number)

11826289817049165713…48310248232909330549

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.365 × 10⁹⁷(98-digit number)

23652579634098331427…96620496465818661099

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

4.730 × 10⁹⁷(98-digit number)

47305159268196662855…93240992931637322199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

9.461 × 10⁹⁷(98-digit number)

94610318536393325711…86481985863274644399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.892 × 10⁹⁸(99-digit number)

18922063707278665142…72963971726549288799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

3.784 × 10⁹⁸(99-digit number)

37844127414557330284…45927943453098577599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

7.568 × 10⁹⁸(99-digit number)

75688254829114660568…91855886906197155199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.513 × 10⁹⁹(100-digit number)

15137650965822932113…83711773812394310399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

3.027 × 10⁹⁹(100-digit number)

30275301931645864227…67423547624788620799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

6.055 × 10⁹⁹(100-digit number)

60550603863291728455…34847095249577241599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^10 × origin − 1

1.211 × 10¹⁰⁰(101-digit number)

12110120772658345691…69694190499154483199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^11 × origin − 1

2.422 × 10¹⁰⁰(101-digit number)

24220241545316691382…39388380998308966399

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 12 consecutive prime numbers forming a Cunningham Chain of the First Kind. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★★★☆

Rarity

ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …

Cross-reference on Chainz Explorer