Block #82,776

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/25/2013, 3:55:12 PM · Difficulty 9.2761 · 6,715,923 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

7147c4403e3b2400ba04a70c27176e751288722b9ec15e326c1ac0a64bb9d075

View on Chainz ↗

Height

#82,776

Difficulty

9.276143

Transactions

Size

210 B

Version

Bits

0946b150

Nonce

105,240

Timestamp

7/25/2013, 3:55:12 PM

Confirmations

6,715,923

Mined by

⛏️ P2SHAeUfKg5rxRST8rJL87myXPCma62tA9YiwL

Merkle Root

dc3559ad2dd98001a0e31a12044e5b27ba2b59d01b5b939bbda3a79b5b129d04

Transactions (1)

Coinbasedc3559ad2dd980…a3a79b5b129d04

1 in → 1 out11.6000 XPM109 B

AeUfKg5r…2tA9YiwL

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.

2.341 × 10¹²¹(122-digit number)

23414937127863782116…96482085445860851411

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

2.341 × 10¹²¹(122-digit number)

23414937127863782116…96482085445860851411

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

4.682 × 10¹²¹(122-digit number)

46829874255727564233…92964170891721702821

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

9.365 × 10¹²¹(122-digit number)

93659748511455128466…85928341783443405641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.873 × 10¹²²(123-digit number)

18731949702291025693…71856683566886811281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

3.746 × 10¹²²(123-digit number)

37463899404582051386…43713367133773622561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

7.492 × 10¹²²(123-digit number)

74927798809164102773…87426734267547245121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.498 × 10¹²³(124-digit number)

14985559761832820554…74853468535094490241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

2.997 × 10¹²³(124-digit number)

29971119523665641109…49706937070188980481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

5.994 × 10¹²³(124-digit number)

59942239047331282218…99413874140377960961

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 Second 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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …

Cross-reference on Chainz Explorer