XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,160,443

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/14/2017, 2:16:22 PM Β· Difficulty 10.9019 Β· 4,647,593 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
6d509de4e91995a14018b10aa4a3f3a647b6d35d2eb457c8a166868fa1c7047a
View on Chainz β†—

Height

#2,160,443

Difficulty

10.901868

Transactions

3

Size

6.53 KB

Version

2

Bits

0ae6e0d9

Nonce

20,114,807

Timestamp

6/14/2017, 2:16:22 PM

Confirmations

4,647,593

Mined by

⛏️ P2SHAVk9xeRXRh3UKCxm1MyxaU4WuLhTRobzjG

Merkle Root

6f5b05617eb6f12563c7f45962cbd3c8214bb14c88b04b8d87ff702c8b1b7705
Transactions (3)
Coinbase9c4c01e91f4632…3b3cd7b6a94c44
1 in β†’ 1 out8.4700 XPM110 B
AVk9xeRX…hTRobzjG
e87daabf9eb7c4…d07020e79c73bd
38 in β†’ 1 out1891.9900 XPM5.54 KB
AcxhUhX6…N8N8w2tm
b2d724afde95b4…6a3ab9e296f49f
5 in β†’ 2 out1.3896 XPM817 B
ATkTCD9N…DZd7hmJmAe5DMz3V…sXmQz5kj
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.

6.742 Γ— 10⁹⁴(95-digit number)
67426142705861791741…16606690053886414199
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
6.742 Γ— 10⁹⁴(95-digit number)
67426142705861791741…16606690053886414199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.742 Γ— 10⁹⁴(95-digit number)
67426142705861791741…16606690053886414201
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
1.348 Γ— 10⁹⁡(96-digit number)
13485228541172358348…33213380107772828399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.348 Γ— 10⁹⁡(96-digit number)
13485228541172358348…33213380107772828401
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
2.697 Γ— 10⁹⁡(96-digit number)
26970457082344716696…66426760215545656799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.697 Γ— 10⁹⁡(96-digit number)
26970457082344716696…66426760215545656801
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
5.394 Γ— 10⁹⁡(96-digit number)
53940914164689433393…32853520431091313599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.394 Γ— 10⁹⁡(96-digit number)
53940914164689433393…32853520431091313601
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
1.078 Γ— 10⁹⁢(97-digit number)
10788182832937886678…65707040862182627199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.078 Γ— 10⁹⁢(97-digit number)
10788182832937886678…65707040862182627201
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.

β˜…β˜…β˜†β˜†β˜†
Rarity
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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
Cross-reference on Chainz Explorer
Circulating Supply:57,708,333 XPMΒ·at block #6,808,035 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.
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