XPM Prime Explorer symbol
XPMPrime Explorer

Block #1,419,341

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/19/2016, 3:09:15 AM Β· Difficulty 10.7918 Β· 5,425,916 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
45861b4398e6c59c0000ec2871e8ed92a38e98a9766fc9a26956557e5626689b
View on Chainz β†—

Height

#1,419,341

Difficulty

10.791822

Transactions

1

Size

199 B

Version

2

Bits

0acab4d1

Nonce

648,456,574

Timestamp

1/19/2016, 3:09:15 AM

Confirmations

5,425,916

Mined by

⛏️ P2SHANvvb2LppspuC4t2xVsF22JPbm2Zf4Thdj

Merkle Root

869ce3baeba84ae7f87b4b159f3023d9c04fb7897f919fe4025d2ccf03028619
Transactions (1)
Coinbase869ce3baeba84a…5d2ccf03028619
1 in β†’ 1 out8.5700 XPM109 B
ANvvb2Lp…2Zf4Thdj
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.

3.449 Γ— 10⁹⁡(96-digit number)
34491032600161796779…54944919360242038399
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
3.449 Γ— 10⁹⁡(96-digit number)
34491032600161796779…54944919360242038399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.449 Γ— 10⁹⁡(96-digit number)
34491032600161796779…54944919360242038401
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
6.898 Γ— 10⁹⁡(96-digit number)
68982065200323593559…09889838720484076799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.898 Γ— 10⁹⁡(96-digit number)
68982065200323593559…09889838720484076801
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
1.379 Γ— 10⁹⁢(97-digit number)
13796413040064718711…19779677440968153599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.379 Γ— 10⁹⁢(97-digit number)
13796413040064718711…19779677440968153601
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
2.759 Γ— 10⁹⁢(97-digit number)
27592826080129437423…39559354881936307199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.759 Γ— 10⁹⁢(97-digit number)
27592826080129437423…39559354881936307201
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
5.518 Γ— 10⁹⁢(97-digit number)
55185652160258874847…79118709763872614399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.518 Γ— 10⁹⁢(97-digit number)
55185652160258874847…79118709763872614401
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:58,006,489 XPMΒ·at block #6,845,256 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