XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #2,142,109

Block #2,142,109

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/2/2017, 5:16:56 PM Β· Difficulty 10.8739 Β· 4,698,270 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
8467e3f54b73b7a3b0e65eef53a8b2fc806e8a74b7f6640ff48d218c3e0b25ac
View on Chainz β†—

Difficulty

10.873899

Transactions

1

Size

200 B

Version

2

Bits

0adfb7d0

Nonce

509,958,269

Timestamp

6/2/2017, 5:16:56 PM

Confirmations

4,698,270

Merkle Root

ca39bd2cc5e3bee28bdd46cc3623aceca57c2ec0355e8dec778e90c7f9ab2ff3
Transactions (1)
Coinbaseca39bd2cc5e3be…8e90c7f9ab2ff3
1 in β†’ 1 out8.4400 XPM110 B
AVbMiqmc…T7L3FzsK
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.

4.966 Γ— 10⁹⁴(95-digit number)
49663130906662901811…58948116124789529280
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
4.966 Γ— 10⁹⁴(95-digit number)
49663130906662901811…58948116124789529281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
9.932 Γ— 10⁹⁴(95-digit number)
99326261813325803623…17896232249579058561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.986 Γ— 10⁹⁡(96-digit number)
19865252362665160724…35792464499158117121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.973 Γ— 10⁹⁡(96-digit number)
39730504725330321449…71584928998316234241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.946 Γ— 10⁹⁡(96-digit number)
79461009450660642899…43169857996632468481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.589 Γ— 10⁹⁢(97-digit number)
15892201890132128579…86339715993264936961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.178 Γ— 10⁹⁢(97-digit number)
31784403780264257159…72679431986529873921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.356 Γ— 10⁹⁢(97-digit number)
63568807560528514319…45358863973059747841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.271 Γ— 10⁹⁷(98-digit number)
12713761512105702863…90717727946119495681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.542 Γ— 10⁹⁷(98-digit number)
25427523024211405727…81435455892238991361
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 2142109

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 8467e3f54b73b7a3b0e65eef53a8b2fc806e8a74b7f6640ff48d218c3e0b25ac

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 #2,142,109 on Chainz β†—
Circulating Supply:57,967,352 XPMΒ·at block #6,840,378 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