Block #680,637

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 8/16/2014, 9:03:45 PM · Difficulty 10.9624 · 6,133,445 confirmations

1CC

Cunningham Chain of the First Kind

A sequence where each prime is double the previous prime plus one.

Block Header

Block Hash

d5f9588a625dbc854c19edb59d3e2e8d1548148327a810120824c0ef63c15050

View on Chainz ↗

Height

#680,637

Difficulty

10.962399

Transactions

Size

243 B

Version

Bits

0af65fcd

Nonce

3,047,918,148

Timestamp

8/16/2014, 9:03:45 PM

Confirmations

6,133,445

Mined by

⛏️ P2SHATrzKxLEMcqj8iissCT2aSSgyrdnfypiwk

Merkle Root

3eac3e4d2c3cb506ff00359d4c3871e7b3af23e514317eedcabf4adc8ef54069

Transactions (1)

Coinbase3eac3e4d2c3cb5…bf4adc8ef54069

1 in → 2 out8.3100 XPM152 B

ATrzKxLE…dnfypiwk ALPu3s2c…EJXLjVFh

Prime Chain Origin

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.

8.532 × 10⁹⁷(98-digit number)

85326663773138556235…45171939114402053119

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

8.532 × 10⁹⁷(98-digit number)

85326663773138556235…45171939114402053119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.706 × 10⁹⁸(99-digit number)

17065332754627711247…90343878228804106239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

3.413 × 10⁹⁸(99-digit number)

34130665509255422494…80687756457608212479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

6.826 × 10⁹⁸(99-digit number)

68261331018510844988…61375512915216424959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.365 × 10⁹⁹(100-digit number)

13652266203702168997…22751025830432849919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

2.730 × 10⁹⁹(100-digit number)

27304532407404337995…45502051660865699839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

5.460 × 10⁹⁹(100-digit number)

54609064814808675990…91004103321731399679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.092 × 10¹⁰⁰(101-digit number)

10921812962961735198…82008206643462799359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

2.184 × 10¹⁰⁰(101-digit number)

21843625925923470396…64016413286925598719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

4.368 × 10¹⁰⁰(101-digit number)

43687251851846940792…28032826573851197439

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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

Block #680,637

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