Block #365,668

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/18/2014, 10:12:39 PM · Difficulty 10.4235 · 6,443,147 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

659fed7e8749888aa8f0bec35792f056c457d5e8511de69265c2342abd470786

View on Chainz ↗

Height

#365,668

Difficulty

10.423531

Transactions

Size

231 B

Version

Bits

0a6c6c86

Nonce

160,275

Timestamp

1/18/2014, 10:12:39 PM

Confirmations

6,443,147

Mined by

⛏️ P2SHARmAMwyuAi8euPwQcDptyGopF9P7Kn74ZT

Merkle Root

cb35e04fb09eb0dc4d9d1b2a3e2e50e0ffd3d095887461006a0e237fa5bf003a

Transactions (1)

Coinbasecb35e04fb09eb0…0e237fa5bf003a

1 in → 2 out9.1900 XPM137 B

ARmAMwyu…P7Kn74ZT ALfEGCwh…VawujfMm

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.

1.386 × 10¹⁰⁴(105-digit number)

13861507442819782937…99346175574593994239

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

1.386 × 10¹⁰⁴(105-digit number)

13861507442819782937…99346175574593994239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.772 × 10¹⁰⁴(105-digit number)

27723014885639565875…98692351149187988479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

5.544 × 10¹⁰⁴(105-digit number)

55446029771279131750…97384702298375976959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.108 × 10¹⁰⁵(106-digit number)

11089205954255826350…94769404596751953919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

2.217 × 10¹⁰⁵(106-digit number)

22178411908511652700…89538809193503907839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

4.435 × 10¹⁰⁵(106-digit number)

44356823817023305400…79077618387007815679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

8.871 × 10¹⁰⁵(106-digit number)

88713647634046610800…58155236774015631359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.774 × 10¹⁰⁶(107-digit number)

17742729526809322160…16310473548031262719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

3.548 × 10¹⁰⁶(107-digit number)

35485459053618644320…32620947096062525439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

7.097 × 10¹⁰⁶(107-digit number)

70970918107237288640…65241894192125050879

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 #365,668

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