XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #284,200

Block #284,200

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/30/2013, 1:18:53 AM Β· Difficulty 9.9823 Β· 6,510,635 confirmations

TWN
Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header
Block Hash
60f5e9ed210e475465a143679fc4e3a21b14e5f4a7f0f82501e5ff32b0d10bc0
View on Chainz β†—

Height

#284,200

Difficulty

9.982279

Transactions

1

Size

206 B

Version

2

Bits

09fb76aa

Nonce

50,332,494

Timestamp

11/30/2013, 1:18:53 AM

Confirmations

6,510,635

Merkle Root

af7af146fed2371dd597ae29bdd41a6314df06c165952d1f28d04128006979ab
Transactions (1)
Coinbaseaf7af146fed237…d04128006979ab
1 in β†’ 1 out10.0200 XPM116 B
AcLBm5Z9…S683d7c3
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.

2.855 Γ— 10⁹⁡(96-digit number)
28556104547366031330…51694405654102115200
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 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.

Level 0 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
2.855 Γ— 10⁹⁡(96-digit number)
28556104547366031330…51694405654102115199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.855 Γ— 10⁹⁡(96-digit number)
28556104547366031330…51694405654102115201
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
5.711 Γ— 10⁹⁡(96-digit number)
57112209094732062660…03388811308204230399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.711 Γ— 10⁹⁡(96-digit number)
57112209094732062660…03388811308204230401
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
1.142 Γ— 10⁹⁢(97-digit number)
11422441818946412532…06777622616408460799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.142 Γ— 10⁹⁢(97-digit number)
11422441818946412532…06777622616408460801
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
2.284 Γ— 10⁹⁢(97-digit number)
22844883637892825064…13555245232816921599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.284 Γ— 10⁹⁢(97-digit number)
22844883637892825064…13555245232816921601
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
4.568 Γ— 10⁹⁢(97-digit number)
45689767275785650128…27110490465633843199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.568 Γ— 10⁹⁢(97-digit number)
45689767275785650128…27110490465633843201
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Bi-Twin Chain. 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 TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial βˆ’ 1 and p+2 = origin/primorial + 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 284200

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 60f5e9ed210e475465a143679fc4e3a21b14e5f4a7f0f82501e5ff32b0d10bc0

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 #284,200 on Chainz β†—
Circulating Supply:57,602,718 XPMΒ·at block #6,794,834 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