XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,635,346

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 4/29/2018, 5:28:26 AM Β· Difficulty 11.3082 Β· 4,203,140 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
d6ef09f8aa3c32efcdb1d624141127de1abc59ce8294285e6c2e71d095018dd8
View on Chainz β†—

Height

#2,635,346

Difficulty

11.308177

Transactions

2

Size

721 B

Version

2

Bits

0b4ee4b5

Nonce

152,134,751

Timestamp

4/29/2018, 5:28:26 AM

Confirmations

4,203,140

Mined by

⛏️ P2SHAK8MDd5us1kj6s5CattHPvUuXBZ6GKpjdB

Merkle Root

9e3345eb3b970b1d303476fffeeeb0b4813a29f0fd21e3a045041354aece2ad9
Transactions (2)
Coinbase6772e39399f1b4…1a4fa80539faab
1 in β†’ 1 out7.8200 XPM110 B
AK8MDd5u…Z6GKpjdB
0a82e018219d7a…38cc0108da63cb
3 in β†’ 2 out21.9692 XPM521 B
AKmpc5Mo…QN7qpT9uAZ4UnHzJ…PH7NQioA
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.

4.082 Γ— 10⁹⁡(96-digit number)
40828312931543446579…85362288038392627199
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
4.082 Γ— 10⁹⁡(96-digit number)
40828312931543446579…85362288038392627199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.082 Γ— 10⁹⁡(96-digit number)
40828312931543446579…85362288038392627201
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
8.165 Γ— 10⁹⁡(96-digit number)
81656625863086893158…70724576076785254399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.165 Γ— 10⁹⁡(96-digit number)
81656625863086893158…70724576076785254401
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
1.633 Γ— 10⁹⁢(97-digit number)
16331325172617378631…41449152153570508799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.633 Γ— 10⁹⁢(97-digit number)
16331325172617378631…41449152153570508801
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
3.266 Γ— 10⁹⁢(97-digit number)
32662650345234757263…82898304307141017599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.266 Γ— 10⁹⁢(97-digit number)
32662650345234757263…82898304307141017601
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
6.532 Γ— 10⁹⁢(97-digit number)
65325300690469514526…65796608614282035199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.532 Γ— 10⁹⁢(97-digit number)
65325300690469514526…65796608614282035201
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
1.306 Γ— 10⁹⁷(98-digit number)
13065060138093902905…31593217228564070399
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:57,952,160 XPMΒ·at block #6,838,485 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