XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,684,952

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/30/2018, 8:50:23 PM Β· Difficulty 11.6915 Β· 4,147,077 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
dddbc74b350cf94ed17b1f60270873274226c249cab09341b7f8bdbc105f3251
View on Chainz β†—

Height

#2,684,952

Difficulty

11.691503

Transactions

2

Size

1016 B

Version

2

Bits

0bb10659

Nonce

428,360,050

Timestamp

5/30/2018, 8:50:23 PM

Confirmations

4,147,077

Mined by

⛏️ P2SHANRa6dSXkcf2E88ZsxNYGteR2kB5vLmerv

Merkle Root

563c63e18533796aac574a9f6b3b4a4f96991cdd6b583f9e1e06217b8dee09c6
Transactions (2)
Coinbase1e78a5cfe9392f…c1e81af785f328
1 in β†’ 1 out7.3200 XPM109 B
ANRa6dSX…B5vLmerv
48a72e5b1bd74e…d559ee7b077b08
5 in β†’ 2 out151.4819 XPM817 B
AdPWxjLf…P7Pgk6E5AbiZw7N1…HPacQJfk
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.

4.548 Γ— 10⁹⁴(95-digit number)
45486577598597520413…79563706145144207299
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
4.548 Γ— 10⁹⁴(95-digit number)
45486577598597520413…79563706145144207299
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.548 Γ— 10⁹⁴(95-digit number)
45486577598597520413…79563706145144207301
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
9.097 Γ— 10⁹⁴(95-digit number)
90973155197195040827…59127412290288414599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.097 Γ— 10⁹⁴(95-digit number)
90973155197195040827…59127412290288414601
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
1.819 Γ— 10⁹⁡(96-digit number)
18194631039439008165…18254824580576829199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.819 Γ— 10⁹⁡(96-digit number)
18194631039439008165…18254824580576829201
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
3.638 Γ— 10⁹⁡(96-digit number)
36389262078878016331…36509649161153658399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.638 Γ— 10⁹⁡(96-digit number)
36389262078878016331…36509649161153658401
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
7.277 Γ— 10⁹⁡(96-digit number)
72778524157756032662…73019298322307316799
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.277 Γ— 10⁹⁡(96-digit number)
72778524157756032662…73019298322307316801
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
1.455 Γ— 10⁹⁢(97-digit number)
14555704831551206532…46038596644614633599
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:57,900,364 XPMΒ·at block #6,832,028 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