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Block #26,110

2CCLength 8★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/13/2013, 4:19:53 AM · Difficulty 7.9738 · 6,763,936 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

e10157e822acba7fd4eafc42101bcca1c3d1f017f4327b696ff869a80e78ba5f

View on Chainz ↗

Height

#26,110

Difficulty

7.973821

Transactions

Size

197 B

Version

Bits

07f94c51

Nonce

118

Timestamp

7/13/2013, 4:19:53 AM

Confirmations

6,763,936

Merkle Root

bca10cae8ce3489311221f7ffd3c9bfb47ce6fe327bf7abc0cd9c09736dd6bec

Transactions (1)

Coinbasebca10cae8ce348…d9c09736dd6bec

1 in → 1 out15.7100 XPM109 B

APgDktsX…X1wcY24f

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.

1.032 × 10⁸⁹(90-digit number)

10328159768190401006…59153831534171073720

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

1.032 × 10⁸⁹(90-digit number)

10328159768190401006…59153831534171073721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

2.065 × 10⁸⁹(90-digit number)

20656319536380802013…18307663068342147441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

4.131 × 10⁸⁹(90-digit number)

41312639072761604026…36615326136684294881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

8.262 × 10⁸⁹(90-digit number)

82625278145523208053…73230652273368589761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.652 × 10⁹⁰(91-digit number)

16525055629104641610…46461304546737179521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

3.305 × 10⁹⁰(91-digit number)

33050111258209283221…92922609093474359041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

6.610 × 10⁹⁰(91-digit number)

66100222516418566442…85845218186948718081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.322 × 10⁹¹(92-digit number)

13220044503283713288…71690436373897436161

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 8 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 8

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 26110

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 e10157e822acba7fd4eafc42101bcca1c3d1f017f4327b696ff869a80e78ba5f

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 #26,110 on Chainz ↗