Block #246,144

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 11/5/2013, 10:12:40 PM · Difficulty 9.9643 · 6,549,918 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

87f71f7efff133a71d32a7a36065af3f6e6e3d708bbd495feb071edb66b5bebe

View on Chainz ↗

Height

#246,144

Difficulty

9.964345

Transactions

Size

1.48 KB

Version

Bits

09f6df55

Nonce

4,008

Timestamp

11/5/2013, 10:12:40 PM

Confirmations

6,549,918

Mined by

⛏️ Rym5AQDGVS66x4YUbhY3Z3fTFJcuAE1PTWdWkm

Merkle Root

9f4896b78f0455c7092c67f45f5f7f9fe6884ace293ce7c788743c8f702fee75

Transactions (1)

Coinbase9f4896b78f0455…743c8f702fee75

1 in → 40 out10.0400 XPM1.39 KB

AQDGVS66…1PTWdWkm Ac5sZcdP…kzV4eckG AMbCuLHZ…WSoStwkc AGbRhLj1…nZcEQFqQ AJzWx2VD…j4ZSMit5

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.

1.247 × 10¹⁰⁰(101-digit number)

12473909570768676860…25872547637859955199

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

1.247 × 10¹⁰⁰(101-digit number)

12473909570768676860…25872547637859955199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.494 × 10¹⁰⁰(101-digit number)

24947819141537353721…51745095275719910399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

4.989 × 10¹⁰⁰(101-digit number)

49895638283074707442…03490190551439820799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

9.979 × 10¹⁰⁰(101-digit number)

99791276566149414884…06980381102879641599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.995 × 10¹⁰¹(102-digit number)

19958255313229882976…13960762205759283199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

3.991 × 10¹⁰¹(102-digit number)

39916510626459765953…27921524411518566399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

7.983 × 10¹⁰¹(102-digit number)

79833021252919531907…55843048823037132799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.596 × 10¹⁰²(103-digit number)

15966604250583906381…11686097646074265599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

3.193 × 10¹⁰²(103-digit number)

31933208501167812762…23372195292148531199

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