Block #556,481

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 5/22/2014, 7:31:59 AM · Difficulty 10.9626 · 6,235,437 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

ff48e24242181e648b71d6e026b9cefe428d33bc3ae561c26c4b4c9b71b8081f

View on Chainz ↗

Height

#556,481

Difficulty

10.962645

Transactions

Size

433 B

Version

Bits

0af66fe8

Nonce

172,332,061

Timestamp

5/22/2014, 7:31:59 AM

Confirmations

6,235,437

Merkle Root

459db50f43314452f31fc2597843d6eb80786355b5770562dc4c524d7198d704

Transactions (2)

Coinbased4de6581432adb…feda4f23e6be74

1 in → 1 out8.3200 XPM116 B

ANSXnLY2…Sd25TjkD

7e6695839804a8…30f4fc6e247804

1 in → 2 out8.3000 XPM226 B

AZxkSxov…9uoWycVz AdcCptxS…QN3MQQCr

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.

8.974 × 10⁹⁷(98-digit number)

89749642756894973258…11603637234249017441

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

8.974 × 10⁹⁷(98-digit number)

89749642756894973258…11603637234249017441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.794 × 10⁹⁸(99-digit number)

17949928551378994651…23207274468498034881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

3.589 × 10⁹⁸(99-digit number)

35899857102757989303…46414548936996069761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

7.179 × 10⁹⁸(99-digit number)

71799714205515978606…92829097873992139521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.435 × 10⁹⁹(100-digit number)

14359942841103195721…85658195747984279041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

2.871 × 10⁹⁹(100-digit number)

28719885682206391442…71316391495968558081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

5.743 × 10⁹⁹(100-digit number)

57439771364412782885…42632782991937116161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.148 × 10¹⁰⁰(101-digit number)

11487954272882556577…85265565983874232321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

2.297 × 10¹⁰⁰(101-digit number)

22975908545765113154…70531131967748464641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

4.595 × 10¹⁰⁰(101-digit number)

45951817091530226308…41062263935496929281

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 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

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 2CC formula:

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

Cross-reference on Chainz Explorer