XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #2,244,098

Block #2,244,098

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/9/2017, 4:22:17 PM Β· Difficulty 10.9470 Β· 4,594,309 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
40409b3af29be6357b71db87c7362cf215af14f350493b4c32247b3985437c55
View on Chainz β†—

Difficulty

10.947020

Transactions

1

Size

200 B

Version

2

Bits

0af26fe9

Nonce

1,065,155,913

Timestamp

8/9/2017, 4:22:17 PM

Confirmations

4,594,309

Merkle Root

69c05a86beb76899afdb1f10c2610bfb506eb2ea0357c83e2e3c8ea57eb8b984
Transactions (1)
Coinbase69c05a86beb768…3c8ea57eb8b984
1 in β†’ 1 out8.3300 XPM110 B
ALJdD2vJ…vVGj5cds
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.

4.527 Γ— 10⁹⁴(95-digit number)
45277617439676938349…75763008322257332960
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
4.527 Γ— 10⁹⁴(95-digit number)
45277617439676938349…75763008322257332959
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.527 Γ— 10⁹⁴(95-digit number)
45277617439676938349…75763008322257332961
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
9.055 Γ— 10⁹⁴(95-digit number)
90555234879353876699…51526016644514665919
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.055 Γ— 10⁹⁴(95-digit number)
90555234879353876699…51526016644514665921
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
1.811 Γ— 10⁹⁡(96-digit number)
18111046975870775339…03052033289029331839
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.811 Γ— 10⁹⁡(96-digit number)
18111046975870775339…03052033289029331841
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
3.622 Γ— 10⁹⁡(96-digit number)
36222093951741550679…06104066578058663679
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.622 Γ— 10⁹⁡(96-digit number)
36222093951741550679…06104066578058663681
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
7.244 Γ— 10⁹⁡(96-digit number)
72444187903483101359…12208133156117327359
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.244 Γ— 10⁹⁡(96-digit number)
72444187903483101359…12208133156117327361
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
1.448 Γ— 10⁹⁢(97-digit number)
14488837580696620271…24416266312234654719
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 2244098

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 40409b3af29be6357b71db87c7362cf215af14f350493b4c32247b3985437c55

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 #2,244,098 on Chainz β†—
Circulating Supply:57,951,528 XPMΒ·at block #6,838,406 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