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Block #26,109

2CCLength 8★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/13/2013, 4:19:39 AM · Difficulty 7.9738 · 6,764,950 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

e0894fbc8db6134dba8e5c62ab0268921c45a683a1a2bd5519cb6169008ca59c

View on Chainz ↗

Height

#26,109

Difficulty

7.973816

Transactions

Size

196 B

Version

Bits

07f94c01

Nonce

Timestamp

7/13/2013, 4:19:39 AM

Confirmations

6,764,950

Merkle Root

2011d224d375311fd2ffc3254e06e6488fe28d68a4e932e9b7bc033c3f177ce7

Transactions (1)

Coinbase2011d224d37531…bc033c3f177ce7

1 in → 1 out15.7100 XPM108 B

AYePHG6c…71wEfEkt

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.

2.003 × 10⁹⁰(91-digit number)

20039649678078170515…81711666152704726770

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

2.003 × 10⁹⁰(91-digit number)

20039649678078170515…81711666152704726771

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

4.007 × 10⁹⁰(91-digit number)

40079299356156341030…63423332305409453541

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

8.015 × 10⁹⁰(91-digit number)

80158598712312682061…26846664610818907081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.603 × 10⁹¹(92-digit number)

16031719742462536412…53693329221637814161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

3.206 × 10⁹¹(92-digit number)

32063439484925072824…07386658443275628321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

6.412 × 10⁹¹(92-digit number)

64126878969850145648…14773316886551256641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.282 × 10⁹²(93-digit number)

12825375793970029129…29546633773102513281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

2.565 × 10⁹²(93-digit number)

25650751587940058259…59093267546205026561

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 26109

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 e0894fbc8db6134dba8e5c62ab0268921c45a683a1a2bd5519cb6169008ca59c

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 #26,109 on Chainz ↗