XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #1,801,846

Block #1,801,846

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/11/2016, 6:18:41 AM Β· Difficulty 10.7714 Β· 4,998,203 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
7d4e283b916a0c279652600a6068c764b334b82619154a48d915ca508fb25fcc
View on Chainz β†—

Difficulty

10.771357

Transactions

1

Size

200 B

Version

2

Bits

0ac577a2

Nonce

1,338,351,086

Timestamp

10/11/2016, 6:18:41 AM

Confirmations

4,998,203

Merkle Root

e7e12070b394815fc753c454436f8e9c25f43cbbd0aebf7e82e3463e3adb26fd
Transactions (1)
Coinbasee7e12070b39481…e3463e3adb26fd
1 in β†’ 1 out8.6100 XPM110 B
ASdDuPf7…mQZYW1Hs
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.

6.790 Γ— 10⁹³(94-digit number)
67904976159805230854…77921452074112571250
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
6.790 Γ— 10⁹³(94-digit number)
67904976159805230854…77921452074112571251
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.358 Γ— 10⁹⁴(95-digit number)
13580995231961046170…55842904148225142501
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.716 Γ— 10⁹⁴(95-digit number)
27161990463922092341…11685808296450285001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.432 Γ— 10⁹⁴(95-digit number)
54323980927844184683…23371616592900570001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.086 Γ— 10⁹⁡(96-digit number)
10864796185568836936…46743233185801140001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.172 Γ— 10⁹⁡(96-digit number)
21729592371137673873…93486466371602280001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.345 Γ— 10⁹⁡(96-digit number)
43459184742275347747…86972932743204560001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
8.691 Γ— 10⁹⁡(96-digit number)
86918369484550695494…73945865486409120001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.738 Γ— 10⁹⁢(97-digit number)
17383673896910139098…47891730972818240001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.476 Γ— 10⁹⁢(97-digit number)
34767347793820278197…95783461945636480001
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 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 1801846

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 7d4e283b916a0c279652600a6068c764b334b82619154a48d915ca508fb25fcc

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 #1,801,846 on Chainz β†—
Circulating Supply:57,644,452 XPMΒ·at block #6,800,048 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