Block #50,224

2CCLength 8★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/16/2013, 12:11:39 AM · Difficulty 8.8791 · 6,744,310 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

ed21df441f9d1c9e67434fa5ae7db40739999b182e0c1129e6b98681943d5b02

View on Chainz ↗

Height

#50,224

Difficulty

8.879061

Transactions

Size

1.93 KB

Version

Bits

08e10a20

Nonce

138

Timestamp

7/16/2013, 12:11:39 AM

Confirmations

6,744,310

Mined by

⛏️ P2SHAWcZR19YDfHJPAHj3RK8vRBVV7hrVPAYuu

Merkle Root

9faf8ef88ad7f0197b063b2da47d08fbb63f1c6106c602527f3a02e9033fc226

Transactions (2)

Coinbase63d1b4db52d4c8…e0586a5abf747e

1 in → 1 out12.6900 XPM110 B

AWcZR19Y…hrVPAYuu

7bb1a4a533e6c9…bfc46a8c294567

14 in → 2 out235.1300 XPM1.73 KB

ASZGZ7X1…ecUFjTry AVdYgp1Y…ThZT4N3q

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.

1.167 × 10¹⁰⁵(106-digit number)

11670147883136615986…20758091896337985761

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

1.167 × 10¹⁰⁵(106-digit number)

11670147883136615986…20758091896337985761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

2.334 × 10¹⁰⁵(106-digit number)

23340295766273231973…41516183792675971521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

4.668 × 10¹⁰⁵(106-digit number)

46680591532546463947…83032367585351943041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

9.336 × 10¹⁰⁵(106-digit number)

93361183065092927895…66064735170703886081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.867 × 10¹⁰⁶(107-digit number)

18672236613018585579…32129470341407772161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

3.734 × 10¹⁰⁶(107-digit number)

37344473226037171158…64258940682815544321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

7.468 × 10¹⁰⁶(107-digit number)

74688946452074342316…28517881365631088641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.493 × 10¹⁰⁷(108-digit number)

14937789290414868463…57035762731262177281

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 8 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 8

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