Block #265,203

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 11/19/2013, 8:20:01 AM · Difficulty 9.9632 · 6,544,255 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

05f22e8f19e31848dfad2d91b283f16f3b91347d73206280fcd72f1ea4ded5fe

View on Chainz ↗

Height

#265,203

Difficulty

9.963191

Transactions

Size

1.71 KB

Version

Bits

09f693b2

Nonce

14,781

Timestamp

11/19/2013, 8:20:01 AM

Confirmations

6,544,255

Mined by

⛏️ aR!!:AKwcMAcHMxC6hzN9c8RsVfpBWrWGekVdtp

Merkle Root

5ef1cf078f7c144bdc2f6512420442f90fe7214a2d5191301b7f279ff9c33dc7

Transactions (1)

Coinbase5ef1cf078f7c14…7f279ff9c33dc7

1 in → 47 out10.0400 XPM1.62 KB

AKwcMAcH…WGekVdtp APZy8y6E…QZaGQjfp ANHbaxZp…XjnHCJJs AVzhvfTX…ZzNJYq61 AUSGA5VC…GYHbnJtz

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.

1.173 × 10⁹⁸(99-digit number)

11736110594759636206…83335554726904601601

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

1.173 × 10⁹⁸(99-digit number)

11736110594759636206…83335554726904601601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

2.347 × 10⁹⁸(99-digit number)

23472221189519272412…66671109453809203201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

4.694 × 10⁹⁸(99-digit number)

46944442379038544825…33342218907618406401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

9.388 × 10⁹⁸(99-digit number)

93888884758077089650…66684437815236812801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.877 × 10⁹⁹(100-digit number)

18777776951615417930…33368875630473625601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

3.755 × 10⁹⁹(100-digit number)

37555553903230835860…66737751260947251201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

7.511 × 10⁹⁹(100-digit number)

75111107806461671720…33475502521894502401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.502 × 10¹⁰⁰(101-digit number)

15022221561292334344…66951005043789004801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

3.004 × 10¹⁰⁰(101-digit number)

30044443122584668688…33902010087578009601

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

Block #265,203

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