Block #248,862

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 11/7/2013, 3:26:03 PM · Difficulty 9.9662 · 6,568,959 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

69a548bc71a22fbd9f8183f3093fae0b9f4130dd5afad509e4c568d5674b9690

View on Chainz ↗

Height

#248,862

Difficulty

9.966153

Transactions

Size

1.81 KB

Version

Bits

09f755ca

Nonce

19,359

Timestamp

11/7/2013, 3:26:03 PM

Confirmations

6,568,959

Mined by

⛏️ R{AYPyobfj64oj1upRKuFUToAC7gU59cRiYQ

Merkle Root

4c9b3f2c40a89b4806233c3e7fdd3bef638fd10160914e6037f7dbc2f7aded89

Transactions (1)

Coinbase4c9b3f2c40a89b…f7dbc2f7aded89

1 in → 50 out10.0300 XPM1.72 KB

AYPyobfj…U59cRiYQ AdL4ZZDR…2eQtg1T9 ARpndEmc…Hg792kEk AQtzUSwq…htAuF3yC ARR7aRH6…ne3DXGXZ

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.

3.463 × 10⁸⁸(89-digit number)

34631356968907959712…44204396750521449479

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

3.463 × 10⁸⁸(89-digit number)

34631356968907959712…44204396750521449479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

6.926 × 10⁸⁸(89-digit number)

69262713937815919424…88408793501042898959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.385 × 10⁸⁹(90-digit number)

13852542787563183884…76817587002085797919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.770 × 10⁸⁹(90-digit number)

27705085575126367769…53635174004171595839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

5.541 × 10⁸⁹(90-digit number)

55410171150252735539…07270348008343191679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.108 × 10⁹⁰(91-digit number)

11082034230050547107…14540696016686383359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

2.216 × 10⁹⁰(91-digit number)

22164068460101094215…29081392033372766719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

4.432 × 10⁹⁰(91-digit number)

44328136920202188431…58162784066745533439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

8.865 × 10⁹⁰(91-digit number)

88656273840404376863…16325568133491066879

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 #248,862

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