Block #318,406

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 12/18/2013, 8:09:44 AM · Difficulty 10.1617 · 6,485,136 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

c72e1c6309ea356f91f89612f01fc6d209584237079e7bd7de9afbc4c7ea3cf2

View on Chainz ↗

Height

#318,406

Difficulty

10.161678

Transactions

Size

202 B

Version

Bits

0a2963c2

Nonce

18,627

Timestamp

12/18/2013, 8:09:44 AM

Confirmations

6,485,136

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

ec66215ae305d57ddc1f5a350494ee49cec1fc28cd615746d49795db91ad53ec

Transactions (1)

Coinbaseec66215ae305d5…9795db91ad53ec

1 in → 1 out9.6700 XPM110 B

AeKNrjNj…1NEq95Ta

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.

1.301 × 10¹⁰⁰(101-digit number)

13010861623280428831…14625695722906559739

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

1.301 × 10¹⁰⁰(101-digit number)

13010861623280428831…14625695722906559739

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.602 × 10¹⁰⁰(101-digit number)

26021723246560857662…29251391445813119479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

5.204 × 10¹⁰⁰(101-digit number)

52043446493121715325…58502782891626238959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.040 × 10¹⁰¹(102-digit number)

10408689298624343065…17005565783252477919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

2.081 × 10¹⁰¹(102-digit number)

20817378597248686130…34011131566504955839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

4.163 × 10¹⁰¹(102-digit number)

41634757194497372260…68022263133009911679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

8.326 × 10¹⁰¹(102-digit number)

83269514388994744520…36044526266019823359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.665 × 10¹⁰²(103-digit number)

16653902877798948904…72089052532039646719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

3.330 × 10¹⁰²(103-digit number)

33307805755597897808…44178105064079293439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

6.661 × 10¹⁰²(103-digit number)

66615611511195795616…88356210128158586879

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