Block #270,752

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 11/24/2013, 4:52:46 AM · Difficulty 9.9514 · 6,538,253 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

aa7b4914dc90518af677953666ecd7bd2c1a59668c3b5f9c35e87dcbe609d82b

View on Chainz ↗

Height

#270,752

Difficulty

9.951394

Transactions

Size

1.91 KB

Version

Bits

09f38e96

Nonce

14,164

Timestamp

11/24/2013, 4:52:46 AM

Confirmations

6,538,253

Mined by

⛏️ !aRAeXR4zCusoKpUPBrR6QqAp34bhM3JoUyt8

Merkle Root

855b6d5e106c00025a9615fb81d18589eaaeeb0bee9cda9a16fb7eebb32c050c

Transactions (1)

Coinbase855b6d5e106c00…fb7eebb32c050c

1 in → 53 out10.0600 XPM1.82 KB

AeXR4zCu…M3JoUyt8 AdL4ZZDR…2eQtg1T9 ARpndEmc…Hg792kEk ANHbaxZp…XjnHCJJs AVzhvfTX…ZzNJYq61

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.

3.813 × 10⁹⁴(95-digit number)

38131305678113997567…12471933888319999999

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

3.813 × 10⁹⁴(95-digit number)

38131305678113997567…12471933888319999999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

7.626 × 10⁹⁴(95-digit number)

76262611356227995134…24943867776639999999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.525 × 10⁹⁵(96-digit number)

15252522271245599026…49887735553279999999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

3.050 × 10⁹⁵(96-digit number)

30505044542491198053…99775471106559999999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

6.101 × 10⁹⁵(96-digit number)

61010089084982396107…99550942213119999999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.220 × 10⁹⁶(97-digit number)

12202017816996479221…99101884426239999999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

2.440 × 10⁹⁶(97-digit number)

24404035633992958443…98203768852479999999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

4.880 × 10⁹⁶(97-digit number)

48808071267985916886…96407537704959999999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

9.761 × 10⁹⁶(97-digit number)

97616142535971833772…92815075409919999999

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 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

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 1CC formula:

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

Cross-reference on Chainz Explorer

Block #270,752

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