Block #252,146

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 11/9/2013, 10:02:07 AM · Difficulty 9.9708 · 6,557,189 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

2d71efa20e5e118f40b70434c27abcf258feff8b2835acad810db7edc3c66542

View on Chainz ↗

Height

#252,146

Difficulty

9.970816

Transactions

Size

2.38 KB

Version

Bits

09f8876d

Nonce

1,020

Timestamp

11/9/2013, 10:02:07 AM

Confirmations

6,557,189

Mined by

⛏️ aR~iAQyr8Lw3A4nTbkdHcAPqKiPptkhs4nt3Pn

Merkle Root

1a296b4f50c6f294a18c8e013bee866fda896dc6816568bc4cc38b7e7c664bfc

Transactions (1)

Coinbase1a296b4f50c6f2…c38b7e7c664bfc

1 in → 67 out10.0100 XPM2.29 KB

AQyr8Lw3…hs4nt3Pn AK5NySZf…XzNDwZSM ALgGDFyg…tHka2xUd AdnG9gQ7…N9B7mA2p AQtzUSwq…htAuF3yC

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.

7.445 × 10⁹⁷(98-digit number)

74452337990845056091…30428456566194787879

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

7.445 × 10⁹⁷(98-digit number)

74452337990845056091…30428456566194787879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.489 × 10⁹⁸(99-digit number)

14890467598169011218…60856913132389575759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

2.978 × 10⁹⁸(99-digit number)

29780935196338022436…21713826264779151519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

5.956 × 10⁹⁸(99-digit number)

59561870392676044872…43427652529558303039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.191 × 10⁹⁹(100-digit number)

11912374078535208974…86855305059116606079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

2.382 × 10⁹⁹(100-digit number)

23824748157070417949…73710610118233212159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

4.764 × 10⁹⁹(100-digit number)

47649496314140835898…47421220236466424319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

9.529 × 10⁹⁹(100-digit number)

95298992628281671796…94842440472932848639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.905 × 10¹⁰⁰(101-digit number)

19059798525656334359…89684880945865697279

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 #252,146

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