Block #259,197

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 11/13/2013, 11:59:03 AM · Difficulty 9.9771 · 6,532,927 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

359972d3206fc31a4c201a083300dccde4155dff29e0463c7aaa5e18228d1493

View on Chainz ↗

Height

#259,197

Difficulty

9.977076

Transactions

Size

391 B

Version

Bits

09fa219f

Nonce

84,962

Timestamp

11/13/2013, 11:59:03 AM

Confirmations

6,532,927

Merkle Root

1da963dd4a75d13624abd3c547ebf43e0751757fd87005f9f9dd72610afb0ea5

Transactions (2)

Coinbase81c7d74a4a9f94…878432cf7e3819

1 in → 1 out10.0400 XPM110 B

AeKNrjNj…1NEq95Ta

3b1bdd613cf3fe…0fdb4599ca153d

1 in → 1 out109.6777 XPM191 B

APH3Qiac…89d34WiU

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.

1.325 × 10⁹⁵(96-digit number)

13258000361733088619…76501367925327127679

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

1.325 × 10⁹⁵(96-digit number)

13258000361733088619…76501367925327127679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.651 × 10⁹⁵(96-digit number)

26516000723466177238…53002735850654255359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

5.303 × 10⁹⁵(96-digit number)

53032001446932354477…06005471701308510719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.060 × 10⁹⁶(97-digit number)

10606400289386470895…12010943402617021439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

2.121 × 10⁹⁶(97-digit number)

21212800578772941791…24021886805234042879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

4.242 × 10⁹⁶(97-digit number)

42425601157545883582…48043773610468085759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

8.485 × 10⁹⁶(97-digit number)

84851202315091767164…96087547220936171519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.697 × 10⁹⁷(98-digit number)

16970240463018353432…92175094441872343039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

3.394 × 10⁹⁷(98-digit number)

33940480926036706865…84350188883744686079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

6.788 × 10⁹⁷(98-digit number)

67880961852073413731…68700377767489372159

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Cunningham Chain of the First 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 1CC formula:

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

Cross-reference on Chainz Explorer