XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #3,077,810

Block #3,077,810

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 3/4/2019, 8:24:55 AM Β· Difficulty 11.0047 Β· 3,763,017 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
67c17a187cc462aa29d4a16ce7e294a91fc70d12061c4dbd156f83bbed1821de
View on Chainz β†—

Difficulty

11.004716

Transactions

2

Size

425 B

Version

2

Bits

0b01350d

Nonce

938,630,663

Timestamp

3/4/2019, 8:24:55 AM

Confirmations

3,763,017

Merkle Root

364ab76221cc1cd38f724a6b3fa775ffbb35ad69c9fa8498c585e128f164031e
Transactions (2)
Coinbasea4697b6297f570…1ad30f4c5b1d9a
1 in β†’ 1 out8.2500 XPM110 B
AbXwmGxD…4XXYP765
107df7ef7f3900…8c2e647ae21f61
1 in β†’ 2 out7.1770 XPM225 B
AbXwmGxD…4XXYP765ALxskxzJ…mwRWwWjn
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.

4.583 Γ— 10⁹⁴(95-digit number)
45833700471686753355…10510058982711780960
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
4.583 Γ— 10⁹⁴(95-digit number)
45833700471686753355…10510058982711780959
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.583 Γ— 10⁹⁴(95-digit number)
45833700471686753355…10510058982711780961
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
9.166 Γ— 10⁹⁴(95-digit number)
91667400943373506710…21020117965423561919
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.166 Γ— 10⁹⁴(95-digit number)
91667400943373506710…21020117965423561921
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
1.833 Γ— 10⁹⁡(96-digit number)
18333480188674701342…42040235930847123839
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.833 Γ— 10⁹⁡(96-digit number)
18333480188674701342…42040235930847123841
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
3.666 Γ— 10⁹⁡(96-digit number)
36666960377349402684…84080471861694247679
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.666 Γ— 10⁹⁡(96-digit number)
36666960377349402684…84080471861694247681
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
7.333 Γ— 10⁹⁡(96-digit number)
73333920754698805368…68160943723388495359
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.333 Γ— 10⁹⁡(96-digit number)
73333920754698805368…68160943723388495361
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
1.466 Γ— 10⁹⁢(97-digit number)
14666784150939761073…36321887446776990719
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 3077810

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 67c17a187cc462aa29d4a16ce7e294a91fc70d12061c4dbd156f83bbed1821de

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 #3,077,810 on Chainz β†—
Circulating Supply:57,970,961 XPMΒ·at block #6,840,826 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