XPM Prime Explorer symbol
XPMPrime Explorer

Block #1,362,235

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/9/2015, 10:33:30 AM Β· Difficulty 10.8434 Β· 5,442,991 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b7e262f7bca0c2c7ddaa13eb3dc6967e2a92bfe74a27c6b1c1c8936c75c72d66
View on Chainz β†—

Height

#1,362,235

Difficulty

10.843442

Transactions

2

Size

10.68 KB

Version

2

Bits

0ad7ebd9

Nonce

889,820,889

Timestamp

12/9/2015, 10:33:30 AM

Confirmations

5,442,991

Mined by

⛏️ P2SHALoZdzw5zomHhZgGzazNJsKBNrGbBLoZKX

Merkle Root

18bcf6a392056158ebfedef19379adf06be36d4eef04ce6f1f92429ed1bcc01e
Transactions (2)
Coinbasef7c743b02341d7…143735cd912237
1 in β†’ 1 out8.6100 XPM110 B
ALoZdzw5…GbBLoZKX
93f1189de1d961…49e49e3e9b0037
72 in β†’ 2 out199.9950 XPM10.48 KB
AVT3G2ZL…XaFq1sZAAQks7JQA…4TWbmuEb
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.

2.898 Γ— 10⁹⁡(96-digit number)
28981391348585253235…50499126209499595519
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
2.898 Γ— 10⁹⁡(96-digit number)
28981391348585253235…50499126209499595519
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.898 Γ— 10⁹⁡(96-digit number)
28981391348585253235…50499126209499595521
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
5.796 Γ— 10⁹⁡(96-digit number)
57962782697170506470…00998252418999191039
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.796 Γ— 10⁹⁡(96-digit number)
57962782697170506470…00998252418999191041
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
1.159 Γ— 10⁹⁢(97-digit number)
11592556539434101294…01996504837998382079
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.159 Γ— 10⁹⁢(97-digit number)
11592556539434101294…01996504837998382081
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
2.318 Γ— 10⁹⁢(97-digit number)
23185113078868202588…03993009675996764159
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.318 Γ— 10⁹⁢(97-digit number)
23185113078868202588…03993009675996764161
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
4.637 Γ— 10⁹⁢(97-digit number)
46370226157736405176…07986019351993528319
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.637 Γ— 10⁹⁢(97-digit number)
46370226157736405176…07986019351993528321
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:57,685,882 XPMΒ·at block #6,805,225 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