XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #2,123,719

Block #2,123,719

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/19/2017, 11:03:55 AM Β· Difficulty 10.9171 Β· 4,690,354 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
04abefd949e0bdb2254939b0473e083eed4d04b0f1cd59747ca13c170de7d47b
View on Chainz β†—

Difficulty

10.917064

Transactions

1

Size

199 B

Version

2

Bits

0aeac4b4

Nonce

1,291,540,790

Timestamp

5/19/2017, 11:03:55 AM

Confirmations

4,690,354

Merkle Root

199b03dac187f4507dee3c0444e3be8054af787533da1bb6f425d82e9f992203
Transactions (1)
Coinbase199b03dac187f4…25d82e9f992203
1 in β†’ 1 out8.3800 XPM109 B
AKWLmVbb…75dqbYAr
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.

2.501 Γ— 10⁹⁴(95-digit number)
25012061937296070839…34878042485751715840
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
2.501 Γ— 10⁹⁴(95-digit number)
25012061937296070839…34878042485751715841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.002 Γ— 10⁹⁴(95-digit number)
50024123874592141678…69756084971503431681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.000 Γ— 10⁹⁡(96-digit number)
10004824774918428335…39512169943006863361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.000 Γ— 10⁹⁡(96-digit number)
20009649549836856671…79024339886013726721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.001 Γ— 10⁹⁡(96-digit number)
40019299099673713342…58048679772027453441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.003 Γ— 10⁹⁡(96-digit number)
80038598199347426684…16097359544054906881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.600 Γ— 10⁹⁢(97-digit number)
16007719639869485336…32194719088109813761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.201 Γ— 10⁹⁢(97-digit number)
32015439279738970673…64389438176219627521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.403 Γ— 10⁹⁢(97-digit number)
64030878559477941347…28778876352439255041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.280 Γ— 10⁹⁷(98-digit number)
12806175711895588269…57557752704878510081
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 2123719

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 04abefd949e0bdb2254939b0473e083eed4d04b0f1cd59747ca13c170de7d47b

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 #2,123,719 on Chainz β†—
Circulating Supply:57,756,663 XPMΒ·at block #6,814,072 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