XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #457,231

Block #457,231

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/23/2014, 6:12:51 PM Β· Difficulty 10.4215 Β· 6,338,374 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c9eeb255aaac7875f9cc92b27989fa4f0e6a0e9c3b6fcdbe06bee9e620c391ef
View on Chainz β†—

Height

#457,231

Difficulty

10.421494

Transactions

1

Size

288 B

Version

2

Bits

0a6be707

Nonce

777,782

Timestamp

3/23/2014, 6:12:51 PM

Confirmations

6,338,374

Merkle Root

f06acc9fa65ea3f41b94136f97d4abfabe19f546db096ff59afd07362f8c3bc8
Transactions (1)
Coinbasef06acc9fa65ea3…fd07362f8c3bc8
1 in β†’ 4 out9.1900 XPM199 B
AMVf7Jrg…xd5AVR7CALzzzbUz…2Cb4jSDNAa2Amg89…4rjYrsPZAJno7LX2…vo4wdWtY
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.

1.972 Γ— 10⁹²(93-digit number)
19729820855172930776…87138203065753408000
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
1.972 Γ— 10⁹²(93-digit number)
19729820855172930776…87138203065753407999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.945 Γ— 10⁹²(93-digit number)
39459641710345861553…74276406131506815999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.891 Γ— 10⁹²(93-digit number)
78919283420691723107…48552812263013631999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.578 Γ— 10⁹³(94-digit number)
15783856684138344621…97105624526027263999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.156 Γ— 10⁹³(94-digit number)
31567713368276689243…94211249052054527999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.313 Γ— 10⁹³(94-digit number)
63135426736553378486…88422498104109055999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.262 Γ— 10⁹⁴(95-digit number)
12627085347310675697…76844996208218111999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.525 Γ— 10⁹⁴(95-digit number)
25254170694621351394…53689992416436223999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.050 Γ— 10⁹⁴(95-digit number)
50508341389242702788…07379984832872447999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.010 Γ— 10⁹⁡(96-digit number)
10101668277848540557…14759969665744895999
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 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 457231

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 c9eeb255aaac7875f9cc92b27989fa4f0e6a0e9c3b6fcdbe06bee9e620c391ef

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 #457,231 on Chainz β†—
Circulating Supply:57,608,904 XPMΒ·at block #6,795,604 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