Block #387,905

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 2/3/2014, 11:00:04 AM · Difficulty 10.4150 · 6,417,201 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

a2fe68db138d735e7e06509ae1e8f531ef90154437bbcfaf097ed834ff4f849e

View on Chainz ↗

Height

#387,905

Difficulty

10.415048

Transactions

Size

849 B

Version

Bits

0a6a4096

Nonce

764

Timestamp

2/3/2014, 11:00:04 AM

Confirmations

6,417,201

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

e47361b8a34da93eff0c4b1f39e660e4512b15ed41c3532172742bb8ae1291d7

Transactions (2)

Coinbaseb8ef9ea0294315…c3884e2e7f80e3

1 in → 1 out9.2175 XPM116 B

AbwWkWZt…kawDhufa

a143f1c32ceafb…06ef15da39a536

4 in → 1 out4.3700 XPM636 B

APcai2Ds…fnmaPDbh

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.

1.211 × 10¹¹¹(112-digit number)

12111996248542037404…20916955907799121919

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

1.211 × 10¹¹¹(112-digit number)

12111996248542037404…20916955907799121919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.422 × 10¹¹¹(112-digit number)

24223992497084074809…41833911815598243839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

4.844 × 10¹¹¹(112-digit number)

48447984994168149619…83667823631196487679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

9.689 × 10¹¹¹(112-digit number)

96895969988336299238…67335647262392975359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.937 × 10¹¹²(113-digit number)

19379193997667259847…34671294524785950719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

3.875 × 10¹¹²(113-digit number)

38758387995334519695…69342589049571901439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

7.751 × 10¹¹²(113-digit number)

77516775990669039390…38685178099143802879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.550 × 10¹¹³(114-digit number)

15503355198133807878…77370356198287605759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

3.100 × 10¹¹³(114-digit number)

31006710396267615756…54740712396575211519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

6.201 × 10¹¹³(114-digit number)

62013420792535231512…09481424793150423039

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