XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #15,194

Block #15,194

1CCLength 7β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/11/2013, 6:50:11 PM Β· Difficulty 7.8459 Β· 6,779,523 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
391b519ad6e10ee107e7b44d9fb8089ec04014f95e54ef29c8718d32e692c2c2
View on Chainz β†—

Height

#15,194

Difficulty

7.845853

Transactions

1

Size

196 B

Version

2

Bits

07d889cf

Nonce

62

Timestamp

7/11/2013, 6:50:11 PM

Confirmations

6,779,523

Merkle Root

a171fb049edfac3acc89bcb388b97005878dec917dd4d7d8134b5bba4ae50303
Transactions (1)
Coinbasea171fb049edfac…4b5bba4ae50303
1 in β†’ 1 out16.2200 XPM108 B
ATTAqAZc…NUt7fVRU
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.

4.867 Γ— 10⁸⁹(90-digit number)
48676479364651049307…75319175317358178320
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
4.867 Γ— 10⁸⁹(90-digit number)
48676479364651049307…75319175317358178319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
9.735 Γ— 10⁸⁹(90-digit number)
97352958729302098614…50638350634716356639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.947 Γ— 10⁹⁰(91-digit number)
19470591745860419722…01276701269432713279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.894 Γ— 10⁹⁰(91-digit number)
38941183491720839445…02553402538865426559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
7.788 Γ— 10⁹⁰(91-digit number)
77882366983441678891…05106805077730853119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.557 Γ— 10⁹¹(92-digit number)
15576473396688335778…10213610155461706239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.115 Γ— 10⁹¹(92-digit number)
31152946793376671556…20427220310923412479
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 7 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
CommonChain length 7
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 15194

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 391b519ad6e10ee107e7b44d9fb8089ec04014f95e54ef29c8718d32e692c2c2

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 #15,194 on Chainz β†—
Circulating Supply:57,601,785 XPMΒ·at block #6,794,716 Β· updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK