Block #557,900

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 5/23/2014, 6:16:26 AM · Difficulty 10.9631 · 6,234,874 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

06675963046b1d205257526ecf8a71f6a246be1087e7d98f464dac0524772ba0

View on Chainz ↗

Height

#557,900

Difficulty

10.963088

Transactions

Size

8.49 KB

Version

Bits

0af68ce9

Nonce

159,451,944

Timestamp

5/23/2014, 6:16:26 AM

Confirmations

6,234,874

Merkle Root

d78380467e526610c9d2d1cd090766a0bd89dad4fa9116f1f4c9721896625982

Transactions (3)

Coinbase449c4ccec6e039…28a4dee0c5c98d

1 in → 1 out8.4000 XPM116 B

ANSXnLY2…Sd25TjkD

a067c2e7610f7e…f0cc763aadf1b0

53 in → 2 out156.0196 XPM7.74 KB

AeoSGv7d…iRJG4Fwr AbyoyrCZ…rWAr6Y8P

5c1d64b6835324…ba109c46bc052b

3 in → 4 out9.1202 XPM557 B

AWjvkJwz…JbcQNttY AeKNrjNj…1NEq95Ta AMeyeZ9L…gJoDemgf AZ3PWPr3…T7o8gD2E

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.

2.794 × 10⁹⁷(98-digit number)

27944322683491499144…36320988531655076029

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

2.794 × 10⁹⁷(98-digit number)

27944322683491499144…36320988531655076029

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

5.588 × 10⁹⁷(98-digit number)

55888645366982998288…72641977063310152059

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.117 × 10⁹⁸(99-digit number)

11177729073396599657…45283954126620304119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.235 × 10⁹⁸(99-digit number)

22355458146793199315…90567908253240608239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

4.471 × 10⁹⁸(99-digit number)

44710916293586398631…81135816506481216479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

8.942 × 10⁹⁸(99-digit number)

89421832587172797262…62271633012962432959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.788 × 10⁹⁹(100-digit number)

17884366517434559452…24543266025924865919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

3.576 × 10⁹⁹(100-digit number)

35768733034869118904…49086532051849731839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

7.153 × 10⁹⁹(100-digit number)

71537466069738237809…98173064103699463679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.430 × 10¹⁰⁰(101-digit number)

14307493213947647561…96346128207398927359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^10 × origin − 1

2.861 × 10¹⁰⁰(101-digit number)

28614986427895295123…92692256414797854719

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