Block #321,740

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 12/20/2013, 12:28:34 PM · Difficulty 10.1949 · 6,474,221 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

1762fcbbd6ba2d3fccd27407164bf935e77ef85e462b211b23cd52d831518032

View on Chainz ↗

Height

#321,740

Difficulty

10.194924

Transactions

Size

1006 B

Version

Bits

0a31e689

Nonce

28,813

Timestamp

12/20/2013, 12:28:34 PM

Confirmations

6,474,221

Mined by

⛏️ aR7AMYa8yniBdW9cQpSC81SYyuCY5vRcnFPip

Merkle Root

d3698b13696d63ebf5ccf192c2619b0d0b740ac6f3a40fbaba354f8ab25d57df

Transactions (1)

Coinbased3698b13696d63…354f8ab25d57df

1 in → 25 out9.6100 XPM913 B

AMYa8yni…vRcnFPip Aac9Hjdg…P4ktypc3 Ad9pSzHt…cpJ3y2zz ARy21REr…6pBWtQJ2 AM1wsdX3…NqVu85hE

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.

8.296 × 10¹⁰⁰(101-digit number)

82969889993061411648…21365104075562639359

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

8.296 × 10¹⁰⁰(101-digit number)

82969889993061411648…21365104075562639359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.659 × 10¹⁰¹(102-digit number)

16593977998612282329…42730208151125278719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

3.318 × 10¹⁰¹(102-digit number)

33187955997224564659…85460416302250557439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

6.637 × 10¹⁰¹(102-digit number)

66375911994449129318…70920832604501114879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.327 × 10¹⁰²(103-digit number)

13275182398889825863…41841665209002229759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

2.655 × 10¹⁰²(103-digit number)

26550364797779651727…83683330418004459519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

5.310 × 10¹⁰²(103-digit number)

53100729595559303454…67366660836008919039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.062 × 10¹⁰³(104-digit number)

10620145919111860690…34733321672017838079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

2.124 × 10¹⁰³(104-digit number)

21240291838223721381…69466643344035676159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

4.248 × 10¹⁰³(104-digit number)

42480583676447442763…38933286688071352319

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