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Block #90,580

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/31/2013, 6:12:03 AM · Difficulty 9.2394 · 6,721,750 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

1a44fe9ec4010b7d204e0e24e5e551b75d48a7d4a5b7b01bc8076cec2f59c0c9

View on Chainz ↗

Height

#90,580

Difficulty

9.239414

Transactions

Size

205 B

Version

Bits

093d4a3e

Nonce

539,289

Timestamp

7/31/2013, 6:12:03 AM

Confirmations

6,721,750

Merkle Root

3b4d3ee38bb2eac4c566b1e7337ed789b839468b249720b3bfce51ccdef5fb45

Transactions (1)

Coinbase3b4d3ee38bb2ea…ce51ccdef5fb45

1 in → 1 out11.7000 XPM109 B

ARzBzYP9…aaexwuhz

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.

1.552 × 10¹⁰⁹(110-digit number)

15520689126790191690…35011374723215672280

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

1.552 × 10¹⁰⁹(110-digit number)

15520689126790191690…35011374723215672281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

3.104 × 10¹⁰⁹(110-digit number)

31041378253580383381…70022749446431344561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

6.208 × 10¹⁰⁹(110-digit number)

62082756507160766762…40045498892862689121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.241 × 10¹¹⁰(111-digit number)

12416551301432153352…80090997785725378241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.483 × 10¹¹⁰(111-digit number)

24833102602864306705…60181995571450756481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

4.966 × 10¹¹⁰(111-digit number)

49666205205728613410…20363991142901512961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

9.933 × 10¹¹⁰(111-digit number)

99332410411457226820…40727982285803025921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.986 × 10¹¹¹(112-digit number)

19866482082291445364…81455964571606051841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

3.973 × 10¹¹¹(112-digit number)

39732964164582890728…62911929143212103681

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.

View full Prime Chain Discovery page →

★☆☆☆☆

Rarity

CommonChain length 9

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, …

Verify on a Primecoin Node

Anyone running a Primecoin node can independently verify this block using the following RPC commands. Run these from the primecoin-cli command line or via the debug console in the Primecoin wallet.

1. Get block hash by height

getblockhash 90580

Returns the block hash for a given block height. Use this to confirm the hash shown above matches the chain.

2. Get full block data

getblock 1a44fe9ec4010b7d204e0e24e5e551b75d48a7d4a5b7b01bc8076cec2f59c0c9

Returns the full block header including difficulty, prime chain origin, prime chain type, transaction IDs, and all other fields shown on this page.

How to run these commands: To verify this data independently, open a terminal on your own Primecoin node and run primecoin-cli <command>. Alternatively, open the Primecoin-Qt wallet, go to Help → Debug Window → Console, and type the command directly. The node must be fully synced to this block height for the commands to return results.

Cross-reference on Chainz Explorer

Chainz is an independent Primecoin block explorer. Compare this block's data to verify accuracy.

View Block #90,580 on Chainz ↗

Block #90,580

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