XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #451,097

Block #451,097

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 3/19/2014, 4:44:12 PM Β· Difficulty 10.3840 Β· 6,388,991 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
af7b78d7da8720a51f5e89664e8f78d4d91b53d7f2ff5d7d41254157deaecd77
View on Chainz β†—

Height

#451,097

Difficulty

10.383966

Transactions

1

Size

206 B

Version

2

Bits

0a624b9e

Nonce

1,556,087,406

Timestamp

3/19/2014, 4:44:12 PM

Confirmations

6,388,991

Merkle Root

b96344a55bb83fd85df0596d8048350c9cb58f6e7e5f7f257a8d31e60c174ea5
Transactions (1)
Coinbaseb96344a55bb83f…8d31e60c174ea5
1 in β†’ 1 out9.2600 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.

2.203 Γ— 10⁹⁡(96-digit number)
22036835983271218427…61612071722345447680
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
2.203 Γ— 10⁹⁡(96-digit number)
22036835983271218427…61612071722345447679
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.203 Γ— 10⁹⁡(96-digit number)
22036835983271218427…61612071722345447681
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
4.407 Γ— 10⁹⁡(96-digit number)
44073671966542436855…23224143444690895359
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.407 Γ— 10⁹⁡(96-digit number)
44073671966542436855…23224143444690895361
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
8.814 Γ— 10⁹⁡(96-digit number)
88147343933084873711…46448286889381790719
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.814 Γ— 10⁹⁡(96-digit number)
88147343933084873711…46448286889381790721
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
1.762 Γ— 10⁹⁢(97-digit number)
17629468786616974742…92896573778763581439
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.762 Γ— 10⁹⁢(97-digit number)
17629468786616974742…92896573778763581441
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
3.525 Γ— 10⁹⁢(97-digit number)
35258937573233949484…85793147557527162879
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.525 Γ— 10⁹⁢(97-digit number)
35258937573233949484…85793147557527162881
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 451097

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 af7b78d7da8720a51f5e89664e8f78d4d91b53d7f2ff5d7d41254157deaecd77

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 #451,097 on Chainz β†—
Circulating Supply:57,965,013 XPMΒ·at block #6,840,087 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