XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #482,266

Block #482,266

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/9/2014, 9:50:11 AM Β· Difficulty 10.5418 Β· 6,318,280 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
a720d5f4ba205876217fe9dfe3213bc6a795e95966cf8af9b0bc485b83ebde08
View on Chainz β†—

Height

#482,266

Difficulty

10.541807

Transactions

1

Size

207 B

Version

2

Bits

0a8ab3e4

Nonce

117,451

Timestamp

4/9/2014, 9:50:11 AM

Confirmations

6,318,280

Merkle Root

aa3d8e3d3fc9cd76bf1a25ac5ea32503027738f789938448b5caa3360e734983
Transactions (1)
Coinbaseaa3d8e3d3fc9cd…caa3360e734983
1 in β†’ 1 out8.9800 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.

2.161 Γ— 10⁹⁸(99-digit number)
21619258179386391874…70497267335116448160
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
2.161 Γ— 10⁹⁸(99-digit number)
21619258179386391874…70497267335116448159
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.161 Γ— 10⁹⁸(99-digit number)
21619258179386391874…70497267335116448161
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
4.323 Γ— 10⁹⁸(99-digit number)
43238516358772783748…40994534670232896319
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.323 Γ— 10⁹⁸(99-digit number)
43238516358772783748…40994534670232896321
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
8.647 Γ— 10⁹⁸(99-digit number)
86477032717545567497…81989069340465792639
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.647 Γ— 10⁹⁸(99-digit number)
86477032717545567497…81989069340465792641
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
1.729 Γ— 10⁹⁹(100-digit number)
17295406543509113499…63978138680931585279
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.729 Γ— 10⁹⁹(100-digit number)
17295406543509113499…63978138680931585281
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
3.459 Γ— 10⁹⁹(100-digit number)
34590813087018226998…27956277361863170559
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.459 Γ— 10⁹⁹(100-digit number)
34590813087018226998…27956277361863170561
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 482266

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 a720d5f4ba205876217fe9dfe3213bc6a795e95966cf8af9b0bc485b83ebde08

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 #482,266 on Chainz β†—
Circulating Supply:57,648,431 XPMΒ·at block #6,800,545 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