XPM Prime Explorer symbol
XPMPrime Explorer

Block #278,262

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/27/2013, 10:04:41 PM Β· Difficulty 9.9685 Β· 6,518,024 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
31ea8b0d36e34fc9de56b84070f236b754bebbb1770e22ae445030cd47aab24e
View on Chainz β†—

Height

#278,262

Difficulty

9.968474

Transactions

1

Size

207 B

Version

2

Bits

09f7edeb

Nonce

103,500

Timestamp

11/27/2013, 10:04:41 PM

Confirmations

6,518,024

Mined by

⛏️ P2SHAcLBm5Z9BD7o7btAchFh9KZEkSS683d7c3

Merkle Root

3aa42ba78773b87bb432bd501dcf44059ab93d836d6201bc3059e6c7040e8080
Transactions (1)
Coinbase3aa42ba78773b8…59e6c7040e8080
1 in β†’ 1 out10.0500 XPM116 B
AcLBm5Z9…S683d7c3
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.

1.925 Γ— 10⁹⁢(97-digit number)
19255535475337552704…09776587064898260479
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
1.925 Γ— 10⁹⁢(97-digit number)
19255535475337552704…09776587064898260479
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.925 Γ— 10⁹⁢(97-digit number)
19255535475337552704…09776587064898260481
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
3.851 Γ— 10⁹⁢(97-digit number)
38511070950675105409…19553174129796520959
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.851 Γ— 10⁹⁢(97-digit number)
38511070950675105409…19553174129796520961
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
7.702 Γ— 10⁹⁢(97-digit number)
77022141901350210818…39106348259593041919
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.702 Γ— 10⁹⁢(97-digit number)
77022141901350210818…39106348259593041921
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
1.540 Γ— 10⁹⁷(98-digit number)
15404428380270042163…78212696519186083839
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.540 Γ— 10⁹⁷(98-digit number)
15404428380270042163…78212696519186083841
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
3.080 Γ— 10⁹⁷(98-digit number)
30808856760540084327…56425393038372167679
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.080 Γ— 10⁹⁷(98-digit number)
30808856760540084327…56425393038372167681
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:57,614,291 XPMΒ·at block #6,796,285 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