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Home/Chain Registry/Block #1,831,994

Block #1,831,994

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/1/2016, 9:56:48 PM Β· Difficulty 10.7212 Β· 4,994,882 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
796f1e4288b27e5e4fd3d838ce31e5730fb063e105ef0cd781e0683465cff455
View on Chainz β†—

Difficulty

10.721204

Transactions

1

Size

199 B

Version

2

Bits

0ab8a0d1

Nonce

1,763,344,690

Timestamp

11/1/2016, 9:56:48 PM

Confirmations

4,994,882

Merkle Root

01785deee4f24d1ee4fae6da3fded432f98485d5d9e8e42ef181f6a34b413752
Transactions (1)
Coinbase01785deee4f24d…81f6a34b413752
1 in β†’ 1 out8.6900 XPM109 B
AWk9zZrZ…MXTzacDn
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.

4.690 Γ— 10⁹⁴(95-digit number)
46903330727558721123…74577837266750886400
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
4.690 Γ— 10⁹⁴(95-digit number)
46903330727558721123…74577837266750886399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
9.380 Γ— 10⁹⁴(95-digit number)
93806661455117442246…49155674533501772799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.876 Γ— 10⁹⁡(96-digit number)
18761332291023488449…98311349067003545599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.752 Γ— 10⁹⁡(96-digit number)
37522664582046976898…96622698134007091199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
7.504 Γ— 10⁹⁡(96-digit number)
75045329164093953797…93245396268014182399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.500 Γ— 10⁹⁢(97-digit number)
15009065832818790759…86490792536028364799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.001 Γ— 10⁹⁢(97-digit number)
30018131665637581519…72981585072056729599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.003 Γ— 10⁹⁢(97-digit number)
60036263331275163038…45963170144113459199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.200 Γ— 10⁹⁷(98-digit number)
12007252666255032607…91926340288226918399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.401 Γ— 10⁹⁷(98-digit number)
24014505332510065215…83852680576453836799
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 1831994

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 796f1e4288b27e5e4fd3d838ce31e5730fb063e105ef0cd781e0683465cff455

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 #1,831,994 on Chainz β†—
Circulating Supply:57,859,172 XPMΒ·at block #6,826,875 Β· updates every 60s
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