XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #2,129,403

Block #2,129,403

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/23/2017, 4:28:17 PM Β· Difficulty 10.9104 Β· 4,711,862 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
65daaa39651d6243732a75b0ec1dd99137196fbdf54d22ce1696a5b1811c8d85
View on Chainz β†—

Difficulty

10.910410

Transactions

1

Size

242 B

Version

2

Bits

0ae9109d

Nonce

258,958,250

Timestamp

5/23/2017, 4:28:17 PM

Confirmations

4,711,862

Merkle Root

196e6b365b899b603706c28225463a07c13d96ea0bd7ff849dcd38a227c8416a
Transactions (1)
Coinbase196e6b365b899b…cd38a227c8416a
1 in β†’ 2 out8.3900 XPM152 B
AK6BxZXL…UXnxyXDBALPu3s2c…EJXLjVFh
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.

1.946 Γ— 10⁹⁡(96-digit number)
19468191129166905157…81163769428897697820
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
1.946 Γ— 10⁹⁡(96-digit number)
19468191129166905157…81163769428897697821
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.893 Γ— 10⁹⁡(96-digit number)
38936382258333810315…62327538857795395641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.787 Γ— 10⁹⁡(96-digit number)
77872764516667620630…24655077715590791281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.557 Γ— 10⁹⁢(97-digit number)
15574552903333524126…49310155431181582561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.114 Γ— 10⁹⁢(97-digit number)
31149105806667048252…98620310862363165121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.229 Γ— 10⁹⁢(97-digit number)
62298211613334096504…97240621724726330241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.245 Γ— 10⁹⁷(98-digit number)
12459642322666819300…94481243449452660481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.491 Γ— 10⁹⁷(98-digit number)
24919284645333638601…88962486898905320961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.983 Γ— 10⁹⁷(98-digit number)
49838569290667277203…77924973797810641921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
9.967 Γ— 10⁹⁷(98-digit number)
99677138581334554407…55849947595621283841
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 2129403

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 65daaa39651d6243732a75b0ec1dd99137196fbdf54d22ce1696a5b1811c8d85

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 #2,129,403 on Chainz β†—
Circulating Supply:57,974,485 XPMΒ·at block #6,841,264 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