XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #3,468,747

Block #3,468,747

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 12/9/2019, 8:00:41 PM Β· Difficulty 10.9790 Β· 3,376,045 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
0e8c71b2e07301689db8890223bebd4f3ad4104c44e92b36f353d72a2126bdd6
View on Chainz β†—

Difficulty

10.978990

Transactions

2

Size

1.43 KB

Version

2

Bits

0afa9f1a

Nonce

913,046,042

Timestamp

12/9/2019, 8:00:41 PM

Confirmations

3,376,045

Merkle Root

81254160fa92a5fd03f7cb23ddae79216cfabc3f17a8db7a4cb250cc60f671c3
Transactions (2)
Coinbasebfdbcc70e7562d…339889b4e251dc
1 in β†’ 1 out8.3000 XPM110 B
ASiq2qtK…VMhmk7yL
c936d0d9ae68e7…bd7c90647b0d4b
8 in β†’ 2 out2693.2336 XPM1.23 KB
ATFEkRSv…6bwekUhEAX3W6pJy…NwZ88svU
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.

1.511 Γ— 10⁹⁡(96-digit number)
15112115740343036609…42357769577593090560
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
1.511 Γ— 10⁹⁡(96-digit number)
15112115740343036609…42357769577593090559
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.511 Γ— 10⁹⁡(96-digit number)
15112115740343036609…42357769577593090561
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
3.022 Γ— 10⁹⁡(96-digit number)
30224231480686073218…84715539155186181119
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.022 Γ— 10⁹⁡(96-digit number)
30224231480686073218…84715539155186181121
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
6.044 Γ— 10⁹⁡(96-digit number)
60448462961372146437…69431078310372362239
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.044 Γ— 10⁹⁡(96-digit number)
60448462961372146437…69431078310372362241
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
1.208 Γ— 10⁹⁢(97-digit number)
12089692592274429287…38862156620744724479
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.208 Γ— 10⁹⁢(97-digit number)
12089692592274429287…38862156620744724481
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
2.417 Γ— 10⁹⁢(97-digit number)
24179385184548858574…77724313241489448959
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.417 Γ— 10⁹⁢(97-digit number)
24179385184548858574…77724313241489448961
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
4.835 Γ— 10⁹⁢(97-digit number)
48358770369097717149…55448626482978897919
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 3468747

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 0e8c71b2e07301689db8890223bebd4f3ad4104c44e92b36f353d72a2126bdd6

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 #3,468,747 on Chainz β†—
Circulating Supply:58,002,749 XPMΒ·at block #6,844,791 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