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Home/Chain Registry/Block #3,082,329

Block #3,082,329

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 3/7/2019, 10:15:56 AM Β· Difficulty 11.0217 Β· 3,755,670 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
98c203c247ad4b882eb76da97dd8d95a6c3d224ef69c5e338020d8f1b39a650f
View on Chainz β†—

Difficulty

11.021708

Transactions

1

Size

199 B

Version

2

Bits

0b058ea1

Nonce

636,940,138

Timestamp

3/7/2019, 10:15:56 AM

Confirmations

3,755,670

Merkle Root

49ada2e63ec1bbd2c4561e3f1c031e86d609b73f1f957de3c6f47b85302ed50b
Transactions (1)
Coinbase49ada2e63ec1bb…f47b85302ed50b
1 in β†’ 1 out8.2200 XPM109 B
AbXwmGxD…4XXYP765
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.

3.316 Γ— 10⁹⁡(96-digit number)
33164395758460057661…33009171261845348480
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
3.316 Γ— 10⁹⁡(96-digit number)
33164395758460057661…33009171261845348481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.632 Γ— 10⁹⁡(96-digit number)
66328791516920115323…66018342523690696961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.326 Γ— 10⁹⁢(97-digit number)
13265758303384023064…32036685047381393921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.653 Γ— 10⁹⁢(97-digit number)
26531516606768046129…64073370094762787841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.306 Γ— 10⁹⁢(97-digit number)
53063033213536092258…28146740189525575681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.061 Γ— 10⁹⁷(98-digit number)
10612606642707218451…56293480379051151361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.122 Γ— 10⁹⁷(98-digit number)
21225213285414436903…12586960758102302721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.245 Γ— 10⁹⁷(98-digit number)
42450426570828873806…25173921516204605441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
8.490 Γ— 10⁹⁷(98-digit number)
84900853141657747613…50347843032409210881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.698 Γ— 10⁹⁸(99-digit number)
16980170628331549522…00695686064818421761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
3.396 Γ— 10⁹⁸(99-digit number)
33960341256663099045…01391372129636843521
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 3082329

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 98c203c247ad4b882eb76da97dd8d95a6c3d224ef69c5e338020d8f1b39a650f

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 #3,082,329 on Chainz β†—
Circulating Supply:57,948,343 XPMΒ·at block #6,837,998 Β· updates every 60s
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