Block #551,756

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 5/19/2014, 1:01:39 AM · Difficulty 10.9624 · 6,254,506 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

6d4ec755a5e03bea2fb4973c7a4a8fc1882eb14a2cd9b20dc4484103d6ef7f94

View on Chainz ↗

Height

#551,756

Difficulty

10.962366

Transactions

Size

244 B

Version

Bits

0af65da5

Nonce

927,141,565

Timestamp

5/19/2014, 1:01:39 AM

Confirmations

6,254,506

Mined by

⛏️ P2SHARzmpY4cAhz8WiJkMBTqRELns6fvx8bF9t

Merkle Root

757d321f11e80be218f9b4c0569b0d42c71f78739f16443df6c0fc7cf625ec14

Transactions (1)

Coinbase757d321f11e80b…c0fc7cf625ec14

1 in → 2 out8.3100 XPM152 B

ARzmpY4c…fvx8bF9t ALPu3s2c…EJXLjVFh

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.

1.222 × 10¹⁰⁰(101-digit number)

12229804946017369575…98216787618959298559

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

1.222 × 10¹⁰⁰(101-digit number)

12229804946017369575…98216787618959298559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.445 × 10¹⁰⁰(101-digit number)

24459609892034739150…96433575237918597119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

4.891 × 10¹⁰⁰(101-digit number)

48919219784069478300…92867150475837194239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

9.783 × 10¹⁰⁰(101-digit number)

97838439568138956600…85734300951674388479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.956 × 10¹⁰¹(102-digit number)

19567687913627791320…71468601903348776959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

3.913 × 10¹⁰¹(102-digit number)

39135375827255582640…42937203806697553919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

7.827 × 10¹⁰¹(102-digit number)

78270751654511165280…85874407613395107839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.565 × 10¹⁰²(103-digit number)

15654150330902233056…71748815226790215679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

3.130 × 10¹⁰²(103-digit number)

31308300661804466112…43497630453580431359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

6.261 × 10¹⁰²(103-digit number)

62616601323608932224…86995260907160862719

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

Block #551,756

Cookie Preferences