Block #11,341

1CCLength 7★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 7/11/2013, 6:17:45 AM · Difficulty 7.7147 · 6,778,135 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

f43cb289c9deafb118b6a70614f502d712c7beaada3923881419126b3045e508

View on Chainz ↗

Height

#11,341

Difficulty

7.714671

Transactions

Size

194 B

Version

Bits

07b6f4b4

Nonce

400

Timestamp

7/11/2013, 6:17:45 AM

Confirmations

6,778,135

Merkle Root

16e21c68a48b7b42a3f9bb9e5397779a3647ff0da1ebb08a278efe9099516de7

Transactions (1)

Coinbase16e21c68a48b7b…8efe9099516de7

1 in → 1 out16.7800 XPM108 B

ARgzrLDZ…JgenLgwi

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.

6.054 × 10⁸⁵(86-digit number)

60540160391309510207…43423233204792477199

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

6.054 × 10⁸⁵(86-digit number)

60540160391309510207…43423233204792477199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.210 × 10⁸⁶(87-digit number)

12108032078261902041…86846466409584954399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

2.421 × 10⁸⁶(87-digit number)

24216064156523804082…73692932819169908799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

4.843 × 10⁸⁶(87-digit number)

48432128313047608165…47385865638339817599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

9.686 × 10⁸⁶(87-digit number)

96864256626095216331…94771731276679635199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.937 × 10⁸⁷(88-digit number)

19372851325219043266…89543462553359270399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

3.874 × 10⁸⁷(88-digit number)

38745702650438086532…79086925106718540799

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 7 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 7

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