XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #403,565

Block #403,565

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 2/14/2014, 6:37:47 AM Β· Difficulty 10.4293 Β· 6,414,103 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
8eb8e2c9e9191af428e08e501defc6ae73a49c19ed80067aa0ce26d009263d4d
View on Chainz β†—

Height

#403,565

Difficulty

10.429307

Transactions

1

Size

222 B

Version

2

Bits

0a6de70b

Nonce

202,250

Timestamp

2/14/2014, 6:37:47 AM

Confirmations

6,414,103

Merkle Root

4dfb3c729399260a79f61de0c9a474e45e1e2e5d851528d0f5208c9c8cf7747e
Transactions (1)
Coinbase4dfb3c72939926…208c9c8cf7747e
1 in β†’ 2 out9.1800 XPM131 B
Ac2JYASP…tcBL5PEWAJno7LX2…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.

1.809 Γ— 10⁹⁷(98-digit number)
18090227091719557032…41013858157459429280
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
1.809 Γ— 10⁹⁷(98-digit number)
18090227091719557032…41013858157459429279
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.809 Γ— 10⁹⁷(98-digit number)
18090227091719557032…41013858157459429281
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
3.618 Γ— 10⁹⁷(98-digit number)
36180454183439114065…82027716314918858559
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.618 Γ— 10⁹⁷(98-digit number)
36180454183439114065…82027716314918858561
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
7.236 Γ— 10⁹⁷(98-digit number)
72360908366878228131…64055432629837717119
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.236 Γ— 10⁹⁷(98-digit number)
72360908366878228131…64055432629837717121
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
1.447 Γ— 10⁹⁸(99-digit number)
14472181673375645626…28110865259675434239
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.447 Γ— 10⁹⁸(99-digit number)
14472181673375645626…28110865259675434241
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
2.894 Γ— 10⁹⁸(99-digit number)
28944363346751291252…56221730519350868479
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.894 Γ— 10⁹⁸(99-digit number)
28944363346751291252…56221730519350868481
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
5.788 Γ— 10⁹⁸(99-digit number)
57888726693502582505…12443461038701736959
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 403565

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 8eb8e2c9e9191af428e08e501defc6ae73a49c19ed80067aa0ce26d009263d4d

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 #403,565 on Chainz β†—
Circulating Supply:57,785,399 XPMΒ·at block #6,817,667 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