XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,118,595

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 5/16/2017, 5:28:44 AM Β· Difficulty 10.9088 Β· 4,714,598 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
00506f31061eae67f9d86df624d58638d925552fa711dfe397a4777fab657d10
View on Chainz β†—

Height

#2,118,595

Difficulty

10.908814

Transactions

1

Size

210 B

Version

2

Bits

0ae8a808

Nonce

154,424,578

Timestamp

5/16/2017, 5:28:44 AM

Confirmations

4,714,598

Mined by

⛏️ P2SHAM6GYpjwZFjhLNzHZAfmRp8jwiaw86QDtR

Merkle Root

3034d6139686a8f94b550d7fe230a00398499d9bf321ba307a16fd0da32fed3d
Transactions (1)
Coinbase3034d6139686a8…16fd0da32fed3d
1 in β†’ 1 out8.3900 XPM118 B
AM6GYpjw…aw86QDtR
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.

3.761 Γ— 10⁹⁸(99-digit number)
37611375889262620192…90946500048562216959
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
3.761 Γ— 10⁹⁸(99-digit number)
37611375889262620192…90946500048562216959
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.761 Γ— 10⁹⁸(99-digit number)
37611375889262620192…90946500048562216961
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
7.522 Γ— 10⁹⁸(99-digit number)
75222751778525240385…81893000097124433919
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.522 Γ— 10⁹⁸(99-digit number)
75222751778525240385…81893000097124433921
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
1.504 Γ— 10⁹⁹(100-digit number)
15044550355705048077…63786000194248867839
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.504 Γ— 10⁹⁹(100-digit number)
15044550355705048077…63786000194248867841
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
3.008 Γ— 10⁹⁹(100-digit number)
30089100711410096154…27572000388497735679
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.008 Γ— 10⁹⁹(100-digit number)
30089100711410096154…27572000388497735681
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
6.017 Γ— 10⁹⁹(100-digit number)
60178201422820192308…55144000776995471359
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.017 Γ— 10⁹⁹(100-digit number)
60178201422820192308…55144000776995471361
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:57,909,729 XPMΒ·at block #6,833,192 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