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Home/Chain Registry/Block #2,825,517

Block #2,825,517

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/5/2018, 7:43:55 AM Β· Difficulty 11.7095 Β· 4,018,015 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
30d3fca040748cd81cc6ceafa43c935b0d72e1c9d744f0b3b065f294b51ba833
View on Chainz β†—

Difficulty

11.709545

Transactions

1

Size

200 B

Version

2

Bits

0bb5a4b7

Nonce

1,275,464,182

Timestamp

9/5/2018, 7:43:55 AM

Confirmations

4,018,015

Merkle Root

5a36c3cb8f15adb0873f74a002af611433f6445465fd7d1805b51cf594e16b79
Transactions (1)
Coinbase5a36c3cb8f15ad…b51cf594e16b79
1 in β†’ 1 out7.2800 XPM110 B
ARdh37Mr…Fr6PdK32
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.316 Γ— 10⁹⁴(95-digit number)
13165219832026989764…73784494348873445480
Discovered Prime Numbers
p_k = 2^k Γ— 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.

1
origin + 1
1.316 Γ— 10⁹⁴(95-digit number)
13165219832026989764…73784494348873445481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.633 Γ— 10⁹⁴(95-digit number)
26330439664053979528…47568988697746890961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.266 Γ— 10⁹⁴(95-digit number)
52660879328107959057…95137977395493781921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.053 Γ— 10⁹⁡(96-digit number)
10532175865621591811…90275954790987563841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.106 Γ— 10⁹⁡(96-digit number)
21064351731243183623…80551909581975127681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.212 Γ— 10⁹⁡(96-digit number)
42128703462486367246…61103819163950255361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
8.425 Γ— 10⁹⁡(96-digit number)
84257406924972734492…22207638327900510721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.685 Γ— 10⁹⁢(97-digit number)
16851481384994546898…44415276655801021441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.370 Γ— 10⁹⁢(97-digit number)
33702962769989093797…88830553311602042881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.740 Γ— 10⁹⁢(97-digit number)
67405925539978187594…77661106623204085761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.348 Γ— 10⁹⁷(98-digit number)
13481185107995637518…55322213246408171521
Verify on FactorDB β†—Wolfram Alpha β†—

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 β€” the large number shown above β€” 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 β†’
β˜…β˜…β˜…β˜†β˜†
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 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 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 2825517

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 30d3fca040748cd81cc6ceafa43c935b0d72e1c9d744f0b3b065f294b51ba833

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 β†’ Debug Window β†’ 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 #2,825,517 on Chainz β†—
Circulating Supply:57,992,630 XPMΒ·at block #6,843,531 Β· updates every 60s
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