XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,938,521

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 11/25/2018, 12:12:47 PM Β· Difficulty 11.3769 Β· 3,905,918 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
3fa2b1f82f9805bbd382a4c1e618da105799ce0d715846f491ce13b499c39446
View on Chainz β†—

Height

#2,938,521

Difficulty

11.376856

Transactions

2

Size

1.14 KB

Version

2

Bits

0b6079a6

Nonce

1,671,212,019

Timestamp

11/25/2018, 12:12:47 PM

Confirmations

3,905,918

Mined by

⛏️ P2SHAbXwmGxDc5ZxwPwgT1QckjRUmF4XXYP765

Merkle Root

6601b9c804a3d2d803ca652c9b0279fd94b6f261cd0d35f419acdefbcabf340e
Transactions (2)
Coinbase993deb4cec1b93…018be53de9d513
1 in β†’ 1 out7.7400 XPM109 B
AbXwmGxD…4XXYP765
0033edede8d789…003c44255c7371
6 in β†’ 2 out1478.5185 XPM964 B
AeoYRFM9…akPhgXp7AZCp4fEP…Dax2ZgNA
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.

4.394 Γ— 10⁹³(94-digit number)
43943444573545371750…95133817144332280599
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
4.394 Γ— 10⁹³(94-digit number)
43943444573545371750…95133817144332280599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.394 Γ— 10⁹³(94-digit number)
43943444573545371750…95133817144332280601
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
8.788 Γ— 10⁹³(94-digit number)
87886889147090743500…90267634288664561199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.788 Γ— 10⁹³(94-digit number)
87886889147090743500…90267634288664561201
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
1.757 Γ— 10⁹⁴(95-digit number)
17577377829418148700…80535268577329122399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.757 Γ— 10⁹⁴(95-digit number)
17577377829418148700…80535268577329122401
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
3.515 Γ— 10⁹⁴(95-digit number)
35154755658836297400…61070537154658244799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.515 Γ— 10⁹⁴(95-digit number)
35154755658836297400…61070537154658244801
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
7.030 Γ— 10⁹⁴(95-digit number)
70309511317672594800…22141074309316489599
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.030 Γ— 10⁹⁴(95-digit number)
70309511317672594800…22141074309316489601
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
1.406 Γ— 10⁹⁡(96-digit number)
14061902263534518960…44282148618632979199
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.

β˜…β˜…β˜…β˜†β˜†
Rarity
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,999,908 XPMΒ·at block #6,844,438 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