XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #3,155,366

Block #3,155,366

TWNLength 12β˜…β˜…β˜…β˜…β˜†

Bi-Twin Chain Β· Discovered 4/25/2019, 9:21:55 PM Β· Difficulty 11.3197 Β· 3,689,105 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
e42e78d38af5d32b5e8b5955dee3091bbc9367a4369b4dc64b6453b637cc736a
View on Chainz β†—

Difficulty

11.319696

Transactions

1

Size

201 B

Version

2

Bits

0b51d795

Nonce

179,799,842

Timestamp

4/25/2019, 9:21:55 PM

Confirmations

3,689,105

Merkle Root

57ef97ac16b46f7bdb29e4bf2e53edb4dd5e4b068d672cb23d1844f9071df503
Transactions (1)
Coinbase57ef97ac16b46f…1844f9071df503
1 in β†’ 1 out7.7900 XPM110 B
AbXwmGxD…4XXYP765
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.

2.641 Γ— 10⁹⁢(97-digit number)
26410397477326734513…53672861286762964480
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
2.641 Γ— 10⁹⁢(97-digit number)
26410397477326734513…53672861286762964479
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.641 Γ— 10⁹⁢(97-digit number)
26410397477326734513…53672861286762964481
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
5.282 Γ— 10⁹⁢(97-digit number)
52820794954653469026…07345722573525928959
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.282 Γ— 10⁹⁢(97-digit number)
52820794954653469026…07345722573525928961
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
1.056 Γ— 10⁹⁷(98-digit number)
10564158990930693805…14691445147051857919
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.056 Γ— 10⁹⁷(98-digit number)
10564158990930693805…14691445147051857921
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
2.112 Γ— 10⁹⁷(98-digit number)
21128317981861387610…29382890294103715839
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.112 Γ— 10⁹⁷(98-digit number)
21128317981861387610…29382890294103715841
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
4.225 Γ— 10⁹⁷(98-digit number)
42256635963722775220…58765780588207431679
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.225 Γ— 10⁹⁷(98-digit number)
42256635963722775220…58765780588207431681
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
8.451 Γ— 10⁹⁷(98-digit number)
84513271927445550441…17531561176414863359
Verify on FactorDB β†—Wolfram Alpha β†—
2^5 Γ— origin + 1
8.451 Γ— 10⁹⁷(98-digit number)
84513271927445550441…17531561176414863361
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^5 Γ— origin + 1 βˆ’ 2^5 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 12 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
ExceptionalChain length 12
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 3155366

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 e42e78d38af5d32b5e8b5955dee3091bbc9367a4369b4dc64b6453b637cc736a

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 #3,155,366 on Chainz β†—
Circulating Supply:58,000,163 XPMΒ·at block #6,844,470 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