XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,147,078

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/5/2017, 2:44:21 PM Β· Difficulty 10.8926 Β· 4,683,424 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
e4944892fe6ad2b4e7e9faaf9020852ac7b5b80b9dd25148c99985e672259f69
View on Chainz β†—

Height

#2,147,078

Difficulty

10.892592

Transactions

2

Size

5.01 KB

Version

2

Bits

0ae480eb

Nonce

993,683,627

Timestamp

6/5/2017, 2:44:21 PM

Confirmations

4,683,424

Mined by

⛏️ P2SHAS9L5UHS9ZcpFiS37EQqPekvWGtp9LRiW6

Merkle Root

8c5bd412b437e10094ee558dcefb7850b3dca0fc627361676d0896c00a9fc428
Transactions (2)
Coinbase5b07f3c1e0da19…111b6617f8b656
1 in β†’ 1 out8.4600 XPM109 B
AS9L5UHS…tp9LRiW6
d65a1f02bbe057…932205f82afcb7
33 in β†’ 1 out291.3830 XPM4.81 KB
AbSihS6q…PPdLXDv8
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.

2.081 Γ— 10⁹⁸(99-digit number)
20813139356807757630…04225999933297131519
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
2.081 Γ— 10⁹⁸(99-digit number)
20813139356807757630…04225999933297131519
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.081 Γ— 10⁹⁸(99-digit number)
20813139356807757630…04225999933297131521
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
4.162 Γ— 10⁹⁸(99-digit number)
41626278713615515261…08451999866594263039
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.162 Γ— 10⁹⁸(99-digit number)
41626278713615515261…08451999866594263041
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
8.325 Γ— 10⁹⁸(99-digit number)
83252557427231030523…16903999733188526079
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.325 Γ— 10⁹⁸(99-digit number)
83252557427231030523…16903999733188526081
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
1.665 Γ— 10⁹⁹(100-digit number)
16650511485446206104…33807999466377052159
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.665 Γ— 10⁹⁹(100-digit number)
16650511485446206104…33807999466377052161
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
3.330 Γ— 10⁹⁹(100-digit number)
33301022970892412209…67615998932754104319
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.330 Γ— 10⁹⁹(100-digit number)
33301022970892412209…67615998932754104321
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:57,888,266 XPMΒ·at block #6,830,501 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