Block #73,565

2CCLength 8★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/21/2013, 6:33:31 AM · Difficulty 8.9949 · 6,717,853 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

450814dc63cfb990b87c02a0f5e96ac07da8bbc0c01b3de08c241f8b62348b9a

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Height

#73,565

Difficulty

8.994912

Transactions

Size

204 B

Version

Bits

08feb287

Nonce

228

Timestamp

7/21/2013, 6:33:31 AM

Confirmations

6,717,853

Merkle Root

03d81c02524c83d90eb23c8e3f2151125553ea95a0a2cae2b5c9cc3f9c1d54ef

Transactions (1)

Coinbase03d81c02524c83…c9cc3f9c1d54ef

1 in → 1 out12.3400 XPM110 B

ANCYL9xh…9WyGnqDE

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.

4.751 × 10¹⁰³(104-digit number)

47511364042400507661…92661885403290610641

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

4.751 × 10¹⁰³(104-digit number)

47511364042400507661…92661885403290610641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

9.502 × 10¹⁰³(104-digit number)

95022728084801015323…85323770806581221281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.900 × 10¹⁰⁴(105-digit number)

19004545616960203064…70647541613162442561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

3.800 × 10¹⁰⁴(105-digit number)

38009091233920406129…41295083226324885121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

7.601 × 10¹⁰⁴(105-digit number)

76018182467840812258…82590166452649770241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.520 × 10¹⁰⁵(106-digit number)

15203636493568162451…65180332905299540481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

3.040 × 10¹⁰⁵(106-digit number)

30407272987136324903…30360665810599080961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

6.081 × 10¹⁰⁵(106-digit number)

60814545974272649807…60721331621198161921

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 8 consecutive prime numbers forming a Cunningham Chain of the Second 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 8

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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …

Cross-reference on Chainz Explorer