XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,222,305

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/25/2017, 2:26:37 PM Β· Difficulty 10.9455 Β· 4,621,470 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
72da765beab9fa70af1907bff195a3ab7e725b6abd3b5c0a93aefffa131441c6
View on Chainz β†—

Height

#2,222,305

Difficulty

10.945539

Transactions

2

Size

390 B

Version

2

Bits

0af20eda

Nonce

1,001,579,827

Timestamp

7/25/2017, 2:26:37 PM

Confirmations

4,621,470

Mined by

⛏️ P2SHAcJbyk73rbqiQdLbTNNdJm777Q2FKZYN4A

Merkle Root

12572ac172719f0475c9737bb1572e751aec1d5b5fd54d877eaf1490b22cf0f8
Transactions (2)
Coinbased539811d1bd418…fadfbf2ac4b695
1 in β†’ 1 out8.3400 XPM109 B
AcJbyk73…2FKZYN4A
dccf7dc352fbcc…fec6d073d0d547
1 in β†’ 1 out0.0800 XPM191 B
AbTUTrYT…o8oNr1D7
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.

7.722 Γ— 10⁹⁡(96-digit number)
77226447589545442797…74779597327804908799
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
7.722 Γ— 10⁹⁡(96-digit number)
77226447589545442797…74779597327804908799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.722 Γ— 10⁹⁡(96-digit number)
77226447589545442797…74779597327804908801
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
1.544 Γ— 10⁹⁢(97-digit number)
15445289517909088559…49559194655609817599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.544 Γ— 10⁹⁢(97-digit number)
15445289517909088559…49559194655609817601
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
3.089 Γ— 10⁹⁢(97-digit number)
30890579035818177118…99118389311219635199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.089 Γ— 10⁹⁢(97-digit number)
30890579035818177118…99118389311219635201
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
6.178 Γ— 10⁹⁢(97-digit number)
61781158071636354237…98236778622439270399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.178 Γ— 10⁹⁢(97-digit number)
61781158071636354237…98236778622439270401
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
1.235 Γ— 10⁹⁷(98-digit number)
12356231614327270847…96473557244878540799
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.235 Γ— 10⁹⁷(98-digit number)
12356231614327270847…96473557244878540801
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:57,994,576 XPMΒ·at block #6,843,774 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