Block #72,289

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/20/2013, 11:16:21 PM · Difficulty 8.9939 · 6,717,651 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

674e9842073ccca3e5d36eb2021a0aed4547fa0cf414612754f703921f4ec57f

View on Chainz ↗

Height

#72,289

Difficulty

8.993949

Transactions

Size

202 B

Version

Bits

08fe7378

Nonce

173

Timestamp

7/20/2013, 11:16:21 PM

Confirmations

6,717,651

Merkle Root

690fc74cc3373a811e8322475399f04383c6bdb4aa37804a553640137c446c92

Transactions (1)

Coinbase690fc74cc3373a…3640137c446c92

1 in → 1 out12.3400 XPM110 B

AK1JUKWL…oPR4rN5o

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.

5.605 × 10⁹⁹(100-digit number)

56054933025787435391…28230619402762344511

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

5.605 × 10⁹⁹(100-digit number)

56054933025787435391…28230619402762344511

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.121 × 10¹⁰⁰(101-digit number)

11210986605157487078…56461238805524689021

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

2.242 × 10¹⁰⁰(101-digit number)

22421973210314974156…12922477611049378041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

4.484 × 10¹⁰⁰(101-digit number)

44843946420629948312…25844955222098756081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

8.968 × 10¹⁰⁰(101-digit number)

89687892841259896625…51689910444197512161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.793 × 10¹⁰¹(102-digit number)

17937578568251979325…03379820888395024321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

3.587 × 10¹⁰¹(102-digit number)

35875157136503958650…06759641776790048641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

7.175 × 10¹⁰¹(102-digit number)

71750314273007917300…13519283553580097281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.435 × 10¹⁰²(103-digit number)

14350062854601583460…27038567107160194561

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 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 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 2CC formula:

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

Cross-reference on Chainz Explorer