Block #300,526

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 12/8/2013, 3:44:13 PM · Difficulty 9.9923 · 6,509,291 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

118363198e2a86579e8be489cf484a78b527f6369208688f9357641d48beb8ce

View on Chainz ↗

Height

#300,526

Difficulty

9.992313

Transactions

Size

1.15 KB

Version

Bits

09fe083d

Nonce

5,643

Timestamp

12/8/2013, 3:44:13 PM

Confirmations

6,509,291

Mined by

⛏️ aRTAQwRN8bEjE7sawFBq7N38V9niAV8PsTcY9

Merkle Root

ec98692cd66468debd80aa45486f2ddd3bdc897a2ca02cd6ddcd489d65cdb1d1

Transactions (1)

Coinbaseec98692cd66468…cd489d65cdb1d1

1 in → 30 out9.9800 XPM1.06 KB

AQwRN8bE…V8PsTcY9 AWXYBWKP…qQAoisBJ AHuJ9wYh…BGmgHrKZ AN4Kh25c…MNMSoyyd AKYeJTFm…4cgnFfJH

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.

5.509 × 10⁹⁴(95-digit number)

55094427798214141683…20256809329974696479

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

5.509 × 10⁹⁴(95-digit number)

55094427798214141683…20256809329974696479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.101 × 10⁹⁵(96-digit number)

11018885559642828336…40513618659949392959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

2.203 × 10⁹⁵(96-digit number)

22037771119285656673…81027237319898785919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

4.407 × 10⁹⁵(96-digit number)

44075542238571313346…62054474639797571839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

8.815 × 10⁹⁵(96-digit number)

88151084477142626693…24108949279595143679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.763 × 10⁹⁶(97-digit number)

17630216895428525338…48217898559190287359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

3.526 × 10⁹⁶(97-digit number)

35260433790857050677…96435797118380574719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

7.052 × 10⁹⁶(97-digit number)

70520867581714101354…92871594236761149439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.410 × 10⁹⁷(98-digit number)

14104173516342820270…85743188473522298879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

2.820 × 10⁹⁷(98-digit number)

28208347032685640541…71486376947044597759

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

Block #300,526

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