XPM Prime Explorer symbol
XPMPrime Explorer

Block #1,343,335

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/26/2015, 10:19:13 PM Β· Difficulty 10.8125 Β· 5,481,491 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
c78593d3492052a8f5356946344ec88c61b1367a61239d3ed391d3f1ad231fcf
View on Chainz β†—

Height

#1,343,335

Difficulty

10.812464

Transactions

2

Size

2.87 KB

Version

2

Bits

0acffda2

Nonce

1,093,675,746

Timestamp

11/26/2015, 10:19:13 PM

Confirmations

5,481,491

Mined by

⛏️ P2SHALor3xJQb6aK5mJc9b3sw7cce3swR11eYQ

Merkle Root

d330538fc860f86ab69413640f78fc9b663e01cd99b97fdff220e9e0ca95c092
Transactions (2)
Coinbase4a5c9c9e1b1de1…a959bc17d2cd43
1 in β†’ 1 out8.5700 XPM109 B
ALor3xJQ…swR11eYQ
812235af9a2aec…216e9a150d76f8
18 in β†’ 2 out857.1865 XPM2.68 KB
AZ6ozq6L…Tz2Z4qfxAVC4ncKf…WM8HZEvv
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.

5.726 Γ— 10⁹⁡(96-digit number)
57268376077025973999…81354657404520282879
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
5.726 Γ— 10⁹⁡(96-digit number)
57268376077025973999…81354657404520282879
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.726 Γ— 10⁹⁡(96-digit number)
57268376077025973999…81354657404520282881
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
1.145 Γ— 10⁹⁢(97-digit number)
11453675215405194799…62709314809040565759
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.145 Γ— 10⁹⁢(97-digit number)
11453675215405194799…62709314809040565761
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
2.290 Γ— 10⁹⁢(97-digit number)
22907350430810389599…25418629618081131519
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.290 Γ— 10⁹⁢(97-digit number)
22907350430810389599…25418629618081131521
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
4.581 Γ— 10⁹⁢(97-digit number)
45814700861620779199…50837259236162263039
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.581 Γ— 10⁹⁢(97-digit number)
45814700861620779199…50837259236162263041
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
9.162 Γ— 10⁹⁢(97-digit number)
91629401723241558399…01674518472324526079
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
9.162 Γ— 10⁹⁢(97-digit number)
91629401723241558399…01674518472324526081
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:57,842,687 XPMΒ·at block #6,824,825 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