Block #364,462

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/18/2014, 2:18:50 AM · Difficulty 10.4212 · 6,475,660 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

e4266b8a949269e8ce1d41043f3067e8b9d6d0a206468e3a2a178abe1cebcacd

View on Chainz ↗

Height

#364,462

Difficulty

10.421222

Transactions

Size

230 B

Version

Bits

0a6bd52e

Nonce

6,794

Timestamp

1/18/2014, 2:18:50 AM

Confirmations

6,475,660

Mined by

⛏️ P2SHARmAMwyuAi8euPwQcDptyGopF9P7Kn74ZT

Merkle Root

50c7fcba8983e0e695098f6e82fcab66dec4f6b1971b09dd7d39c6d2d83f33b6

Transactions (1)

Coinbase50c7fcba8983e0…39c6d2d83f33b6

1 in → 2 out9.1900 XPM137 B

ARmAMwyu…P7Kn74ZT AU6kq4CL…dQBLvxLp

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.

4.602 × 10¹⁰²(103-digit number)

46020775525582670526…80932178140638636799

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

4.602 × 10¹⁰²(103-digit number)

46020775525582670526…80932178140638636799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

9.204 × 10¹⁰²(103-digit number)

92041551051165341052…61864356281277273599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.840 × 10¹⁰³(104-digit number)

18408310210233068210…23728712562554547199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

3.681 × 10¹⁰³(104-digit number)

36816620420466136420…47457425125109094399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

7.363 × 10¹⁰³(104-digit number)

73633240840932272841…94914850250218188799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.472 × 10¹⁰⁴(105-digit number)

14726648168186454568…89829700500436377599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

2.945 × 10¹⁰⁴(105-digit number)

29453296336372909136…79659401000872755199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

5.890 × 10¹⁰⁴(105-digit number)

58906592672745818273…59318802001745510399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.178 × 10¹⁰⁵(106-digit number)

11781318534549163654…18637604003491020799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

2.356 × 10¹⁰⁵(106-digit number)

23562637069098327309…37275208006982041599

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 #364,462

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