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Home/Chain Registry/Block #2,682,174

Block #2,682,174

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/28/2018, 10:35:35 PM Β· Difficulty 11.6912 Β· 4,160,538 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
dc71c096a825c472b9d1fe2da33264b1a37d7f45a23db86a8d1094c79e365854
View on Chainz β†—

Difficulty

11.691242

Transactions

1

Size

201 B

Version

2

Bits

0bb0f539

Nonce

103,309,628

Timestamp

5/28/2018, 10:35:35 PM

Confirmations

4,160,538

Merkle Root

0e59d244e3a7ce539905f1b9ffa305e36441ab908affd55be9149c8f44a8785b
Transactions (1)
Coinbase0e59d244e3a7ce…149c8f44a8785b
1 in β†’ 1 out7.3000 XPM110 B
Adqah8zh…1WwoHJ9t
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.

1.114 Γ— 10⁹⁢(97-digit number)
11144329441007867962…64099863627067484160
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
1.114 Γ— 10⁹⁢(97-digit number)
11144329441007867962…64099863627067484159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.228 Γ— 10⁹⁢(97-digit number)
22288658882015735925…28199727254134968319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.457 Γ— 10⁹⁢(97-digit number)
44577317764031471851…56399454508269936639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.915 Γ— 10⁹⁢(97-digit number)
89154635528062943703…12798909016539873279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.783 Γ— 10⁹⁷(98-digit number)
17830927105612588740…25597818033079746559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.566 Γ— 10⁹⁷(98-digit number)
35661854211225177481…51195636066159493119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.132 Γ— 10⁹⁷(98-digit number)
71323708422450354962…02391272132318986239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.426 Γ— 10⁹⁸(99-digit number)
14264741684490070992…04782544264637972479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.852 Γ— 10⁹⁸(99-digit number)
28529483368980141985…09565088529275944959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.705 Γ— 10⁹⁸(99-digit number)
57058966737960283970…19130177058551889919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.141 Γ— 10⁹⁹(100-digit number)
11411793347592056794…38260354117103779839
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 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 2682174

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 dc71c096a825c472b9d1fe2da33264b1a37d7f45a23db86a8d1094c79e365854

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 #2,682,174 on Chainz β†—
Circulating Supply:57,986,033 XPMΒ·at block #6,842,711 Β· updates every 60s
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