Home/Chain Registry/Block #2,668,870

Block #2,668,870

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 5/19/2018, 8:38:29 PM · Difficulty 11.6766 · 4,172,162 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

4c02d955a60e5eb4a55861059a36decc5e9e5cefdb85aa89301fded618c20394

View on Chainz ↗

Height

#2,668,870

Difficulty

11.676585

Transactions

Size

1.19 KB

Version

Bits

0bad34a6

Nonce

193,741,119

Timestamp

5/19/2018, 8:38:29 PM

Confirmations

4,172,162

Merkle Root

83a5d548c266a91f8b05d59f3a68db72e826c419bde83629de0e421c81405d36

Transactions (4)

Coinbase1b271d1e160c8c…5dabb8c8a72038

1 in → 1 out7.3500 XPM110 B

AdtkmvVA…RVp6EicX

d4cf60627fd7b3…df8bddad508bb8

2 in → 2 out12.0100 XPM338 B

AdGiA44u…3LRhpZUV AKD9LeNP…bQTn8mEf

5840f213610025…a3255be9440ccb

2 in → 2 out12.0000 XPM341 B

AW3QZZmg…j2rGjUkp AWVaRpce…gf7tPgYm

c7a9ba720594df…3cb7ba15511f68

2 in → 2 out12.0000 XPM341 B

AXWo3j4c…Q4EKx56i AM6XD26m…RcphfPC1

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.

3.421 × 10⁹³(94-digit number)

34218872364611873179…23966149841650558240

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

3.421 × 10⁹³(94-digit number)

34218872364611873179…23966149841650558241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

6.843 × 10⁹³(94-digit number)

68437744729223746358…47932299683301116481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.368 × 10⁹⁴(95-digit number)

13687548945844749271…95864599366602232961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

2.737 × 10⁹⁴(95-digit number)

27375097891689498543…91729198733204465921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

5.475 × 10⁹⁴(95-digit number)

54750195783378997086…83458397466408931841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.095 × 10⁹⁵(96-digit number)

10950039156675799417…66916794932817863681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

2.190 × 10⁹⁵(96-digit number)

21900078313351598834…33833589865635727361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

4.380 × 10⁹⁵(96-digit number)

43800156626703197669…67667179731271454721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

8.760 × 10⁹⁵(96-digit number)

87600313253406395338…35334359462542909441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

1.752 × 10⁹⁶(97-digit number)

17520062650681279067…70668718925085818881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^10 × origin + 1

3.504 × 10⁹⁶(97-digit number)

35040125301362558135…41337437850171637761

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

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 2668870

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 4c02d955a60e5eb4a55861059a36decc5e9e5cefdb85aa89301fded618c20394

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 #2,668,870 on Chainz ↗

Block #2,668,870

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