XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #645,148

Block #645,148

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/23/2014, 8:04:04 PM Β· Difficulty 10.9541 Β· 6,150,364 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b4826bf79929b9bc8d31024dc49f8965783fce918bc5c1b504e5a72db257cfcc
View on Chainz β†—

Height

#645,148

Difficulty

10.954075

Transactions

3

Size

806 B

Version

2

Bits

0af43e3c

Nonce

713,783,684

Timestamp

7/23/2014, 8:04:04 PM

Confirmations

6,150,364

Merkle Root

7b0c43afcc9672805b4615e687b6fdfb831f8b2596c8e6ec086ff752d8a3c282
Transactions (3)
Coinbase8c064818f2df5d…5b5eea3290e4ba
1 in β†’ 1 out8.3400 XPM116 B
ANSXnLY2…Sd25TjkD
c1f2f4f2f32420…9afcda1c8ea02a
2 in β†’ 2 out15.5864 XPM373 B
AeCqp28Q…8JXKw4YWAV6HPqW8…jGzasrqf
628f6f0814066c…f5b886a8019108
1 in β†’ 2 out7.2839 XPM226 B
AXBGxZt4…9yiN8mpMAQbXQJ4K…SZFydyis
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.

1.856 Γ— 10⁹⁷(98-digit number)
18564008927566791385…00998925313227939840
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
1.856 Γ— 10⁹⁷(98-digit number)
18564008927566791385…00998925313227939839
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.856 Γ— 10⁹⁷(98-digit number)
18564008927566791385…00998925313227939841
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
3.712 Γ— 10⁹⁷(98-digit number)
37128017855133582771…01997850626455879679
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.712 Γ— 10⁹⁷(98-digit number)
37128017855133582771…01997850626455879681
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
7.425 Γ— 10⁹⁷(98-digit number)
74256035710267165542…03995701252911759359
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.425 Γ— 10⁹⁷(98-digit number)
74256035710267165542…03995701252911759361
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
1.485 Γ— 10⁹⁸(99-digit number)
14851207142053433108…07991402505823518719
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.485 Γ— 10⁹⁸(99-digit number)
14851207142053433108…07991402505823518721
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
2.970 Γ— 10⁹⁸(99-digit number)
29702414284106866216…15982805011647037439
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.970 Γ— 10⁹⁸(99-digit number)
29702414284106866216…15982805011647037441
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 645148

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 b4826bf79929b9bc8d31024dc49f8965783fce918bc5c1b504e5a72db257cfcc

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 #645,148 on Chainz β†—
Circulating Supply:57,608,159 XPMΒ·at block #6,795,511 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