Block #89,090

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/30/2013, 3:06:57 AM · Difficulty 9.2598 · 6,719,924 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

409114d54b0c9dc49c7384ed2ada81a8a43f3eff619e0af691658a7ae0c420b9

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Height

#89,090

Difficulty

9.259752

Transactions

Size

205 B

Version

Bits

09427f1d

Nonce

955

Timestamp

7/30/2013, 3:06:57 AM

Confirmations

6,719,924

Mined by

⛏️ P2SHATRTCZskaHRPBjT3pKKipmUABHKXH2HspV

Merkle Root

1ede33e89e1e91a8c5c6d9ce25996f95b29ce84b8de47cce182bbdd69b6139eb

Transactions (1)

Coinbase1ede33e89e1e91…2bbdd69b6139eb

1 in → 1 out11.6500 XPM110 B

ATRTCZsk…KXH2HspV

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.

2.015 × 10¹⁰⁷(108-digit number)

20153140108104097895…97360173298445646951

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

2.015 × 10¹⁰⁷(108-digit number)

20153140108104097895…97360173298445646951

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

4.030 × 10¹⁰⁷(108-digit number)

40306280216208195791…94720346596891293901

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

8.061 × 10¹⁰⁷(108-digit number)

80612560432416391583…89440693193782587801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.612 × 10¹⁰⁸(109-digit number)

16122512086483278316…78881386387565175601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

3.224 × 10¹⁰⁸(109-digit number)

32245024172966556633…57762772775130351201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

6.449 × 10¹⁰⁸(109-digit number)

64490048345933113267…15525545550260702401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.289 × 10¹⁰⁹(110-digit number)

12898009669186622653…31051091100521404801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

2.579 × 10¹⁰⁹(110-digit number)

25796019338373245306…62102182201042809601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

5.159 × 10¹⁰⁹(110-digit number)

51592038676746490613…24204364402085619201

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 Second 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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …

Cross-reference on Chainz Explorer

Block #89,090

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