XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,643,845

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/2/2018, 6:18:55 AM Β· Difficulty 11.6952 Β· 4,199,777 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
7f92e7ca8c335ecd7cc431a54618e75f9cfd9dc7d41689957bd04b964231bc40
View on Chainz β†—

Height

#2,643,845

Difficulty

11.695210

Transactions

1

Size

200 B

Version

2

Bits

0bb1f94e

Nonce

1,404,346,326

Timestamp

5/2/2018, 6:18:55 AM

Confirmations

4,199,777

Mined by

⛏️ P2SHAZ3h4Dbj3UdTxzMk28ZiiCizEhqWD2c6nX

Merkle Root

9024aaf08a09cb15cece56ce053aa3916bb104c1a920e961db815ca54ad75c00
Transactions (1)
Coinbase9024aaf08a09cb…815ca54ad75c00
1 in β†’ 1 out7.3000 XPM110 B
AZ3h4Dbj…qWD2c6nX
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.

6.635 Γ— 10⁹³(94-digit number)
66357058671199580721…30004594885947830719
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
6.635 Γ— 10⁹³(94-digit number)
66357058671199580721…30004594885947830719
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.635 Γ— 10⁹³(94-digit number)
66357058671199580721…30004594885947830721
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
1.327 Γ— 10⁹⁴(95-digit number)
13271411734239916144…60009189771895661439
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.327 Γ— 10⁹⁴(95-digit number)
13271411734239916144…60009189771895661441
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
2.654 Γ— 10⁹⁴(95-digit number)
26542823468479832288…20018379543791322879
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.654 Γ— 10⁹⁴(95-digit number)
26542823468479832288…20018379543791322881
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
5.308 Γ— 10⁹⁴(95-digit number)
53085646936959664576…40036759087582645759
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.308 Γ— 10⁹⁴(95-digit number)
53085646936959664576…40036759087582645761
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
1.061 Γ— 10⁹⁡(96-digit number)
10617129387391932915…80073518175165291519
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.061 Γ— 10⁹⁡(96-digit number)
10617129387391932915…80073518175165291521
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
2.123 Γ— 10⁹⁡(96-digit number)
21234258774783865830…60147036350330583039
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:57,993,342 XPMΒ·at block #6,843,621 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