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Home/Chain Registry/Block #2,647,173

Block #2,647,173

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/3/2018, 7:10:18 PM Β· Difficulty 11.7559 Β· 4,186,741 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
1f38d2f48f72b078f79dff04df6a9a5c10744be746bf01194616489306fd5e07
View on Chainz β†—

Difficulty

11.755871

Transactions

2

Size

49.72 KB

Version

2

Bits

0bc180cb

Nonce

1,275,606,126

Timestamp

5/3/2018, 7:10:18 PM

Confirmations

4,186,741

Merkle Root

03df8f3c530455b7d4809436ff2a1b3795169884ac51c659ba33ed414f4bb9b1
Transactions (2)
Coinbasedcbaefe656d275…dd14257b956421
1 in β†’ 1 out7.7300 XPM110 B
Adqah8zh…1WwoHJ9t
ccb4ced6873b37…746c8f1fde848b
342 in β†’ 2 out115.3821 XPM49.53 KB
ANn4oFyT…PsxDpdJMAJN8r8Aj…M2rFHcg5
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.

2.095 Γ— 10⁹⁴(95-digit number)
20957330043804413055…88751390338833300740
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
2.095 Γ— 10⁹⁴(95-digit number)
20957330043804413055…88751390338833300739
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.191 Γ— 10⁹⁴(95-digit number)
41914660087608826111…77502780677666601479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.382 Γ— 10⁹⁴(95-digit number)
83829320175217652223…55005561355333202959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.676 Γ— 10⁹⁡(96-digit number)
16765864035043530444…10011122710666405919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.353 Γ— 10⁹⁡(96-digit number)
33531728070087060889…20022245421332811839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.706 Γ— 10⁹⁡(96-digit number)
67063456140174121778…40044490842665623679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.341 Γ— 10⁹⁢(97-digit number)
13412691228034824355…80088981685331247359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.682 Γ— 10⁹⁢(97-digit number)
26825382456069648711…60177963370662494719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.365 Γ— 10⁹⁢(97-digit number)
53650764912139297423…20355926741324989439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.073 Γ— 10⁹⁷(98-digit number)
10730152982427859484…40711853482649978879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.146 Γ— 10⁹⁷(98-digit number)
21460305964855718969…81423706965299957759
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 2647173

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 1f38d2f48f72b078f79dff04df6a9a5c10744be746bf01194616489306fd5e07

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 #2,647,173 on Chainz β†—
Circulating Supply:57,915,538 XPMΒ·at block #6,833,913 Β· updates every 60s
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