XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #857,451

Block #857,451

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/17/2014, 8:32:22 PM Β· Difficulty 10.9675 Β· 5,985,383 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c7fa6cceb39ea58c8f100a9391cc808f7434ca03c910926454f851e31e7a7cc6
View on Chainz β†—

Height

#857,451

Difficulty

10.967518

Transactions

2

Size

424 B

Version

2

Bits

0af7af41

Nonce

454,983,299

Timestamp

12/17/2014, 8:32:22 PM

Confirmations

5,985,383

Merkle Root

1a0101ff6268ed0cf7f952c3fddad9f11f79715b0136420e6709875de868eeac
Transactions (2)
Coinbase6072a7ed161ab6…e21511ad2d078e
1 in β†’ 1 out8.3150 XPM109 B
ASFiEMWB…DAD5PkLn
1d4def38e11f53…1d504d7f005a47
1 in β†’ 2 out0.0395 XPM225 B
AYMAQ8bt…Zt4rJzNsAN3teBBn…Jatt9VtK
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.

1.147 Γ— 10⁹⁴(95-digit number)
11479879557723836086…83231665351699701120
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
1.147 Γ— 10⁹⁴(95-digit number)
11479879557723836086…83231665351699701121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.295 Γ— 10⁹⁴(95-digit number)
22959759115447672173…66463330703399402241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.591 Γ— 10⁹⁴(95-digit number)
45919518230895344346…32926661406798804481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.183 Γ— 10⁹⁴(95-digit number)
91839036461790688693…65853322813597608961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.836 Γ— 10⁹⁡(96-digit number)
18367807292358137738…31706645627195217921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.673 Γ— 10⁹⁡(96-digit number)
36735614584716275477…63413291254390435841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.347 Γ— 10⁹⁡(96-digit number)
73471229169432550954…26826582508780871681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.469 Γ— 10⁹⁢(97-digit number)
14694245833886510190…53653165017561743361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.938 Γ— 10⁹⁢(97-digit number)
29388491667773020381…07306330035123486721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.877 Γ— 10⁹⁢(97-digit number)
58776983335546040763…14612660070246973441
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 857451

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 c7fa6cceb39ea58c8f100a9391cc808f7434ca03c910926454f851e31e7a7cc6

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 #857,451 on Chainz β†—
Circulating Supply:57,987,015 XPMΒ·at block #6,842,833 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