Home/Chain Registry/Block #3,054,793

Block #3,054,793

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 2/16/2019, 3:16:39 AM · Difficulty 11.0021 · 3,781,942 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

66e687c542c59ab94f780a65c24e6d7720654b8474423d80a763670d52202dcd

View on Chainz ↗

Height

#3,054,793

Difficulty

11.002093

Transactions

Size

1.74 KB

Version

Bits

0b008930

Nonce

442,228,453

Timestamp

2/16/2019, 3:16:39 AM

Confirmations

3,781,942

Merkle Root

01b7065d56aa6a9c9b354b2638486e9716c6c79735710a2eac4e026bd0e0d3ce

Transactions (4)

Coinbased4ebc5a7a2fd8f…55aba4fe148434

1 in → 1 out8.2800 XPM110 B

AUMQRepm…tAfKmdW1

3c830133c5fd3b…17a3e822f22907

1 in → 2 out8.2400 XPM192 B

AbXwmGxD…4XXYP765 AGbm9W17…Jvw6eg2t

f299559c0b4dd6…155fe3baa23a3a

3 in → 2 out20.7340 XPM456 B

AbXwmGxD…4XXYP765 AMZuxd2i…c7nhFBCg

c7d410f4db2d21…3d2505b2529ad4

6 in → 2 out10.0122 XPM932 B

AbXwmGxD…4XXYP765 ASLDtSak…2wEAFbXG

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.

2.264 × 10⁹⁶(97-digit number)

22643894816960923485…73247741115850777600

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

2.264 × 10⁹⁶(97-digit number)

22643894816960923485…73247741115850777601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

4.528 × 10⁹⁶(97-digit number)

45287789633921846971…46495482231701555201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

9.057 × 10⁹⁶(97-digit number)

90575579267843693943…92990964463403110401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.811 × 10⁹⁷(98-digit number)

18115115853568738788…85981928926806220801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

3.623 × 10⁹⁷(98-digit number)

36230231707137477577…71963857853612441601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

7.246 × 10⁹⁷(98-digit number)

72460463414274955154…43927715707224883201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.449 × 10⁹⁸(99-digit number)

14492092682854991030…87855431414449766401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

2.898 × 10⁹⁸(99-digit number)

28984185365709982061…75710862828899532801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

5.796 × 10⁹⁸(99-digit number)

57968370731419964123…51421725657799065601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

1.159 × 10⁹⁹(100-digit number)

11593674146283992824…02843451315598131201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^10 × origin + 1

2.318 × 10⁹⁹(100-digit number)

23187348292567985649…05686902631196262401

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 3054793

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 66e687c542c59ab94f780a65c24e6d7720654b8474423d80a763670d52202dcd

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 #3,054,793 on Chainz ↗

Block #3,054,793

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