Block #235,611

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 10/31/2013, 12:57:51 AM · Difficulty 9.9458 · 6,572,322 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

685f45fddbc799b38c62484015adf123c1074789dfcfeb2cbcf5bba6a8c08ec7

View on Chainz ↗

Height

#235,611

Difficulty

9.945822

Transactions

Size

2.11 KB

Version

Bits

09f22160

Nonce

808

Timestamp

10/31/2013, 12:57:51 AM

Confirmations

6,572,322

Mined by

⛏️ RqAANo4YY1xjeppLPNm9kAdtJjYCnvnsPRDSU

Merkle Root

f4a2e17e4341fb576e537ec324a8b822de80e3d8f29e48945a1d2f046c808e27

Transactions (1)

Coinbasef4a2e17e4341fb…1d2f046c808e27

1 in → 59 out10.0600 XPM2.02 KB

ANo4YY1x…vnsPRDSU Ae7UyoY4…DtgAv9cY AQtzUSwq…htAuF3yC APgWZwJ2…1nTrECFn AcEnwywz…vZtt2xTs

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.

4.385 × 10⁹⁹(100-digit number)

43859149345686127184…77320769548831237439

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

4.385 × 10⁹⁹(100-digit number)

43859149345686127184…77320769548831237439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

8.771 × 10⁹⁹(100-digit number)

87718298691372254368…54641539097662474879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.754 × 10¹⁰⁰(101-digit number)

17543659738274450873…09283078195324949759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

3.508 × 10¹⁰⁰(101-digit number)

35087319476548901747…18566156390649899519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

7.017 × 10¹⁰⁰(101-digit number)

70174638953097803494…37132312781299799039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.403 × 10¹⁰¹(102-digit number)

14034927790619560698…74264625562599598079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

2.806 × 10¹⁰¹(102-digit number)

28069855581239121397…48529251125199196159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

5.613 × 10¹⁰¹(102-digit number)

56139711162478242795…97058502250398392319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.122 × 10¹⁰²(103-digit number)

11227942232495648559…94117004500796784639

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

Block #235,611

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