Block #237,422

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 11/1/2013, 1:06:06 AM · Difficulty 9.9497 · 6,553,572 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

499e68c766cf031b43c6717278ec582e898aee4c7f37cf69bd7befe314f9c890

View on Chainz ↗

Height

#237,422

Difficulty

9.949671

Transactions

Size

1.39 KB

Version

Bits

09f31da0

Nonce

3,696

Timestamp

11/1/2013, 1:06:06 AM

Confirmations

6,553,572

Merkle Root

8c4a096120ce2bd9b34a4621cdec441941c32f7da84be8cd4e77cff8f78664fd

Transactions (3)

Coinbasee3300a0609d686…97cce3d4eb4f74

1 in → 2 out10.1100 XPM137 B

AZDUEbdS…RYKMRZET AHsw4d6U…EnM8UXNZ

2491c6485a46dd…2183a98bb6c53c

5 in → 2 out4999.9100 XPM819 B

AH9jKJf9…DKv7YQbs AV4p6Twh…VP3UV4Xj

d91c9d61684441…58aee544b6baf3

2 in → 2 out3.3455 XPM373 B

AXhaNbot…iUXbKduX ASnSjgQg…fewAaNPL

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.

1.601 × 10¹⁰⁰(101-digit number)

16017692042648292918…08949089031247005439

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

1.601 × 10¹⁰⁰(101-digit number)

16017692042648292918…08949089031247005439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

3.203 × 10¹⁰⁰(101-digit number)

32035384085296585837…17898178062494010879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

6.407 × 10¹⁰⁰(101-digit number)

64070768170593171675…35796356124988021759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.281 × 10¹⁰¹(102-digit number)

12814153634118634335…71592712249976043519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

2.562 × 10¹⁰¹(102-digit number)

25628307268237268670…43185424499952087039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

5.125 × 10¹⁰¹(102-digit number)

51256614536474537340…86370848999904174079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.025 × 10¹⁰²(103-digit number)

10251322907294907468…72741697999808348159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

2.050 × 10¹⁰²(103-digit number)

20502645814589814936…45483395999616696319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

4.100 × 10¹⁰²(103-digit number)

41005291629179629872…90966791999233392639

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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