Block #568,009

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 5/30/2014, 2:39:11 AM · Difficulty 10.9652 · 6,226,276 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

60b95fbcdddc03279f76ddd39a467d25c4af820353135a6e79862f139757c0c6

View on Chainz ↗

Height

#568,009

Difficulty

10.965174

Transactions

Size

434 B

Version

Bits

0af7159d

Nonce

1,378,605,493

Timestamp

5/30/2014, 2:39:11 AM

Confirmations

6,226,276

Merkle Root

f06e02078c6daa0bf4a156714a6aebad69ded5e87edec4da9e04f42d4232e046

Transactions (2)

Coinbase32b63ce978a384…6d732d11f2302c

1 in → 1 out8.3100 XPM116 B

ANSXnLY2…Sd25TjkD

9ed7813fc48d8a…2ab02189a2d38b

1 in → 2 out3.1001 XPM227 B

ANEziW4o…55otuEEy AQ9iyTCP…XkfuTJPJ

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.

1.568 × 10⁹⁸(99-digit number)

15687255559612082683…84447374104880247679

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

1.568 × 10⁹⁸(99-digit number)

15687255559612082683…84447374104880247679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

3.137 × 10⁹⁸(99-digit number)

31374511119224165366…68894748209760495359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

6.274 × 10⁹⁸(99-digit number)

62749022238448330733…37789496419520990719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.254 × 10⁹⁹(100-digit number)

12549804447689666146…75578992839041981439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

2.509 × 10⁹⁹(100-digit number)

25099608895379332293…51157985678083962879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

5.019 × 10⁹⁹(100-digit number)

50199217790758664586…02315971356167925759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.003 × 10¹⁰⁰(101-digit number)

10039843558151732917…04631942712335851519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

2.007 × 10¹⁰⁰(101-digit number)

20079687116303465834…09263885424671703039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

4.015 × 10¹⁰⁰(101-digit number)

40159374232606931669…18527770849343406079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

8.031 × 10¹⁰⁰(101-digit number)

80318748465213863338…37055541698686812159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^10 × origin − 1

1.606 × 10¹⁰¹(102-digit number)

16063749693042772667…74111083397373624319

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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