Block #80,404

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/24/2013, 3:26:52 AM · Difficulty 9.2494 · 6,710,906 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

dccfe9f0aaa74bcd928e761cecfc058269c8e97d3217d10814298a56aa173132

View on Chainz ↗

Height

#80,404

Difficulty

9.249414

Transactions

Size

1.19 KB

Version

Bits

093fd997

Nonce

435,883

Timestamp

7/24/2013, 3:26:52 AM

Confirmations

6,710,906

Merkle Root

9fc31554e03bb274b9b9c8d6fbc7dfd51b6e07d44ced12e751afe64c33e9ad6e

Transactions (2)

Coinbase9e487493b8c04c…b5a0666024d86d

1 in → 1 out11.6900 XPM109 B

AVsaeeec…NV1QV7Ba

69ed2238281cf4…6bb999fa8ec823

8 in → 2 out84.3500 XPM1.00 KB

AGsc67aR…2SwERLyG AHhg9WyM…nTicvK7Y

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.

1.738 × 10⁹³(94-digit number)

17384796387271322345…40919704910706317101

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

1.738 × 10⁹³(94-digit number)

17384796387271322345…40919704910706317101

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

3.476 × 10⁹³(94-digit number)

34769592774542644691…81839409821412634201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

6.953 × 10⁹³(94-digit number)

69539185549085289382…63678819642825268401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.390 × 10⁹⁴(95-digit number)

13907837109817057876…27357639285650536801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.781 × 10⁹⁴(95-digit number)

27815674219634115753…54715278571301073601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

5.563 × 10⁹⁴(95-digit number)

55631348439268231506…09430557142602147201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.112 × 10⁹⁵(96-digit number)

11126269687853646301…18861114285204294401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

2.225 × 10⁹⁵(96-digit number)

22252539375707292602…37722228570408588801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

4.450 × 10⁹⁵(96-digit number)

44505078751414585204…75444457140817177601

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