Block #302,757

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 12/10/2013, 12:09:02 AM · Difficulty 9.9928 · 6,493,516 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

5858e0c251a606d1822770981020643b3c5b98b189cce46d37f9b169e46f7651

View on Chainz ↗

Height

#302,757

Difficulty

9.992802

Transactions

Size

1.14 KB

Version

Bits

09fe2849

Nonce

12,166

Timestamp

12/10/2013, 12:09:02 AM

Confirmations

6,493,516

Mined by

⛏️ aRAQwRN8bEjE7sawFBq7N38V9niAV8PsTcY9

Merkle Root

3cf7483fc2aab5e7a18c6b36e9c7d022c964b493694a217e3c0ff3fba5972f6c

Transactions (1)

Coinbase3cf7483fc2aab5…0ff3fba5972f6c

1 in → 30 out9.9800 XPM1.06 KB

AQwRN8bE…V8PsTcY9 Ad9pSzHt…cpJ3y2zz AWZd1qVJ…9pj9yfPa ARcqMJhp…RVLToQ6S AJzWx2VD…j4ZSMit5

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.

7.031 × 10⁸⁶(87-digit number)

70318589304109963348…87790971727280511409

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

7.031 × 10⁸⁶(87-digit number)

70318589304109963348…87790971727280511409

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.406 × 10⁸⁷(88-digit number)

14063717860821992669…75581943454561022819

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

2.812 × 10⁸⁷(88-digit number)

28127435721643985339…51163886909122045639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

5.625 × 10⁸⁷(88-digit number)

56254871443287970679…02327773818244091279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.125 × 10⁸⁸(89-digit number)

11250974288657594135…04655547636488182559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

2.250 × 10⁸⁸(89-digit number)

22501948577315188271…09311095272976365119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

4.500 × 10⁸⁸(89-digit number)

45003897154630376543…18622190545952730239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

9.000 × 10⁸⁸(89-digit number)

90007794309260753086…37244381091905460479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.800 × 10⁸⁹(90-digit number)

18001558861852150617…74488762183810920959

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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