Block #81,021

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/24/2013, 11:52:44 AM · Difficulty 9.2655 · 6,708,762 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

ab6fe31697610033fe102c6f0b6459070baa2675d0f65221e85b792afd248407

View on Chainz ↗

Height

#81,021

Difficulty

9.265523

Transactions

Size

1.39 KB

Version

Bits

0943f953

Nonce

Timestamp

7/24/2013, 11:52:44 AM

Confirmations

6,708,762

Merkle Root

f4b373fb11437eb37b4116882a9caa0aad7ab62984975c70042a988e31f943e9

Transactions (3)

Coinbase648422a57ca0d8…d0eafd9547cc08

1 in → 1 out11.6500 XPM110 B

AN239ZSe…PHfu9UZq

83ca2f3c28f03f…c72892f5d0aded

1 in → 2 out26.6200 XPM226 B

AHbLAmZT…ES3ocEbb AHWcrQb5…rLdjPZqL

b6164b15eb90cd…e89adbf44a4605

8 in → 2 out94.5700 XPM992 B

Ac1Cch6j…3bRomfJn Ad4kL7ba…bcxscyCR

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.

1.485 × 10¹⁰⁰(101-digit number)

14858040830395325949…46044730426758582551

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

1.485 × 10¹⁰⁰(101-digit number)

14858040830395325949…46044730426758582551

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

2.971 × 10¹⁰⁰(101-digit number)

29716081660790651899…92089460853517165101

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

5.943 × 10¹⁰⁰(101-digit number)

59432163321581303799…84178921707034330201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.188 × 10¹⁰¹(102-digit number)

11886432664316260759…68357843414068660401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.377 × 10¹⁰¹(102-digit number)

23772865328632521519…36715686828137320801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

4.754 × 10¹⁰¹(102-digit number)

47545730657265043039…73431373656274641601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

9.509 × 10¹⁰¹(102-digit number)

95091461314530086079…46862747312549283201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.901 × 10¹⁰²(103-digit number)

19018292262906017215…93725494625098566401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

3.803 × 10¹⁰²(103-digit number)

38036584525812034431…87450989250197132801

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