Block #78,382

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/22/2013, 7:32:36 PM · Difficulty 9.2325 · 6,716,997 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

096211c7c8f843d4fbff5643a124f83b80f01679bd28f7436b0b535b5a8aeb1c

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Height

#78,382

Difficulty

9.232549

Transactions

Size

211 B

Version

Bits

093b885d

Nonce

Timestamp

7/22/2013, 7:32:36 PM

Confirmations

6,716,997

Mined by

⛏️ P2SHAY6xNPwDghXeFtoHtwwk8MnPKJ6A5tU5GV

Merkle Root

6f15a69f590a920ac28274e74f9a1cd5d15b5f1765990a69d5f219fb6b5e2d77

Transactions (1)

Coinbase6f15a69f590a92…f219fb6b5e2d77

1 in → 1 out11.7100 XPM110 B

AY6xNPwD…6A5tU5GV

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.

1.571 × 10¹²²(123-digit number)

15718619761716096213…34478537375807021381

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

1.571 × 10¹²²(123-digit number)

15718619761716096213…34478537375807021381

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

3.143 × 10¹²²(123-digit number)

31437239523432192426…68957074751614042761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

6.287 × 10¹²²(123-digit number)

62874479046864384853…37914149503228085521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.257 × 10¹²³(124-digit number)

12574895809372876970…75828299006456171041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.514 × 10¹²³(124-digit number)

25149791618745753941…51656598012912342081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

5.029 × 10¹²³(124-digit number)

50299583237491507882…03313196025824684161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.005 × 10¹²⁴(125-digit number)

10059916647498301576…06626392051649368321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

2.011 × 10¹²⁴(125-digit number)

20119833294996603153…13252784103298736641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

4.023 × 10¹²⁴(125-digit number)

40239666589993206306…26505568206597473281

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