XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #331,046

Block #331,046

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/27/2013, 2:43:07 AM Β· Difficulty 10.1662 Β· 6,472,914 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
9a9a7c603e24aad72d9336fdc9171761862bfcbb5348606fe3961437f40760d4
View on Chainz β†—

Height

#331,046

Difficulty

10.166239

Transactions

1

Size

207 B

Version

2

Bits

0a2a8ea2

Nonce

2,728

Timestamp

12/27/2013, 2:43:07 AM

Confirmations

6,472,914

Merkle Root

b0128c1c119a20c74eda6e6f7e3181c03f1c2918bd4315436cfa7e6424f45381
Transactions (1)
Coinbaseb0128c1c119a20…fa7e6424f45381
1 in β†’ 1 out9.6600 XPM116 B
AbwWkWZt…kawDhufa
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.

1.271 Γ— 10⁹⁢(97-digit number)
12713992713255153412…91754436361972653120
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
1.271 Γ— 10⁹⁢(97-digit number)
12713992713255153412…91754436361972653121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.542 Γ— 10⁹⁢(97-digit number)
25427985426510306824…83508872723945306241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.085 Γ— 10⁹⁢(97-digit number)
50855970853020613648…67017745447890612481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.017 Γ— 10⁹⁷(98-digit number)
10171194170604122729…34035490895781224961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.034 Γ— 10⁹⁷(98-digit number)
20342388341208245459…68070981791562449921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.068 Γ— 10⁹⁷(98-digit number)
40684776682416490919…36141963583124899841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
8.136 Γ— 10⁹⁷(98-digit number)
81369553364832981838…72283927166249799681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.627 Γ— 10⁹⁸(99-digit number)
16273910672966596367…44567854332499599361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.254 Γ— 10⁹⁸(99-digit number)
32547821345933192735…89135708664999198721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.509 Γ— 10⁹⁸(99-digit number)
65095642691866385470…78271417329998397441
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 331046

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 9a9a7c603e24aad72d9336fdc9171761862bfcbb5348606fe3961437f40760d4

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 #331,046 on Chainz β†—
Circulating Supply:57,675,732 XPMΒ·at block #6,803,959 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