XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #128,512

Block #128,512

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/22/2013, 6:56:53 AM Β· Difficulty 9.7834 Β· 6,698,570 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
082dab4463afbd11258d5a97d0d0a38864712c52145058bdeb91012eaf708c6a
View on Chainz β†—

Height

#128,512

Difficulty

9.783423

Transactions

1

Size

198 B

Version

2

Bits

09c88e66

Nonce

209,466

Timestamp

8/22/2013, 6:56:53 AM

Confirmations

6,698,570

Merkle Root

f67ee43273c7c94e337b22814aed5c00a51999d34125de8886ce316800da675a
Transactions (1)
Coinbasef67ee43273c7c9…ce316800da675a
1 in β†’ 1 out10.4300 XPM109 B
AcTm5or2…7HPzWFcv
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.

2.005 Γ— 10⁹³(94-digit number)
20055914513925256877…97012819738402119140
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
2.005 Γ— 10⁹³(94-digit number)
20055914513925256877…97012819738402119141
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.011 Γ— 10⁹³(94-digit number)
40111829027850513754…94025639476804238281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.022 Γ— 10⁹³(94-digit number)
80223658055701027508…88051278953608476561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.604 Γ— 10⁹⁴(95-digit number)
16044731611140205501…76102557907216953121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.208 Γ— 10⁹⁴(95-digit number)
32089463222280411003…52205115814433906241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.417 Γ— 10⁹⁴(95-digit number)
64178926444560822006…04410231628867812481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.283 Γ— 10⁹⁡(96-digit number)
12835785288912164401…08820463257735624961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.567 Γ— 10⁹⁡(96-digit number)
25671570577824328802…17640926515471249921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.134 Γ— 10⁹⁡(96-digit number)
51343141155648657605…35281853030942499841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.026 Γ— 10⁹⁢(97-digit number)
10268628231129731521…70563706061884999681
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 128512

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 082dab4463afbd11258d5a97d0d0a38864712c52145058bdeb91012eaf708c6a

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 #128,512 on Chainz β†—
Circulating Supply:57,860,841 XPMΒ·at block #6,827,081 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