XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #1,810,424

Block #1,810,424

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/16/2016, 6:47:27 PM Β· Difficulty 10.7986 Β· 5,032,237 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
ef8dbb2652e212a96887efa15597773b0b09f4ba432b17309dcbf88dbad4a464
View on Chainz β†—

Difficulty

10.798552

Transactions

2

Size

1.28 KB

Version

2

Bits

0acc6de3

Nonce

329,547,323

Timestamp

10/16/2016, 6:47:27 PM

Confirmations

5,032,237

Merkle Root

6cb2c65e88668610f104d4aca9b16efb4d5d7aa95f9e1b98ba1a10425080044d
Transactions (2)
Coinbase5107adfea7bfb4…ac9b3b9095b952
1 in β†’ 1 out8.5800 XPM109 B
AYJWtp89…xvAMG7YE
083cb0a8a095d2…d4d57071734f70
7 in β†’ 2 out821.4082 XPM1.09 KB
ARywRRZa…HVd3P31RAbR97wjn…8Y9oPAp4
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.

1.740 Γ— 10⁹³(94-digit number)
17402798070043030175…99097088947315357440
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
1.740 Γ— 10⁹³(94-digit number)
17402798070043030175…99097088947315357439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.480 Γ— 10⁹³(94-digit number)
34805596140086060351…98194177894630714879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.961 Γ— 10⁹³(94-digit number)
69611192280172120702…96388355789261429759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.392 Γ— 10⁹⁴(95-digit number)
13922238456034424140…92776711578522859519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.784 Γ— 10⁹⁴(95-digit number)
27844476912068848281…85553423157045719039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.568 Γ— 10⁹⁴(95-digit number)
55688953824137696562…71106846314091438079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.113 Γ— 10⁹⁡(96-digit number)
11137790764827539312…42213692628182876159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.227 Γ— 10⁹⁡(96-digit number)
22275581529655078624…84427385256365752319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.455 Γ— 10⁹⁡(96-digit number)
44551163059310157249…68854770512731504639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
8.910 Γ— 10⁹⁡(96-digit number)
89102326118620314499…37709541025463009279
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 1810424

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 ef8dbb2652e212a96887efa15597773b0b09f4ba432b17309dcbf88dbad4a464

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 #1,810,424 on Chainz β†—
Circulating Supply:57,985,723 XPMΒ·at block #6,842,660 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.
Privacy PolicyΒ·
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

Cookie Preferences

We use cookies to enhance your experience. Some are essential for the site to function, while others help us understand how you use the site.

Β·Privacy Policy