Block #79,318

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/23/2013, 9:48:47 AM · Difficulty 9.2455 · 6,711,676 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

7f4d8f455bcb9ee3eca0f296e3364023b19fbfb9909043694d7c3929da573cb4

View on Chainz ↗

Height

#79,318

Difficulty

9.245528

Transactions

Size

1.07 KB

Version

Bits

093edaf2

Nonce

280

Timestamp

7/23/2013, 9:48:47 AM

Confirmations

6,711,676

Merkle Root

7709b5f11c0eaf0e305af7b78336120a37fc20dc8e36c82b71f2b84be26320af

Transactions (3)

Coinbase8b950f8104b162…97988fb08bd9c2

1 in → 1 out11.7000 XPM110 B

AeCyRn4f…eAgKxKMs

a5ec501dba7a9d…424f5c4e00280d

4 in → 2 out365.0114 XPM668 B

AWeWcPM1…BA2a8s16 AYuBTL1n…QiY1Vxr6

5b7a459eb70db4…43785b2f1c63db

1 in → 2 out9.9900 XPM227 B

AaJDAn2M…4GaiGq3Y AHBuUhnD…RpNrR4HF

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.

9.007 × 10⁸⁹(90-digit number)

90074769568800646480…64546882652197494901

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

9.007 × 10⁸⁹(90-digit number)

90074769568800646480…64546882652197494901

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.801 × 10⁹⁰(91-digit number)

18014953913760129296…29093765304394989801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

3.602 × 10⁹⁰(91-digit number)

36029907827520258592…58187530608789979601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

7.205 × 10⁹⁰(91-digit number)

72059815655040517184…16375061217579959201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.441 × 10⁹¹(92-digit number)

14411963131008103436…32750122435159918401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

2.882 × 10⁹¹(92-digit number)

28823926262016206873…65500244870319836801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

5.764 × 10⁹¹(92-digit number)

57647852524032413747…31000489740639673601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.152 × 10⁹²(93-digit number)

11529570504806482749…62000979481279347201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

2.305 × 10⁹²(93-digit number)

23059141009612965499…24001958962558694401

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