XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,618,426

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 4/17/2018, 7:23:47 PM Β· Difficulty 11.2395 Β· 4,211,983 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
3e0e2c2a779b8054134a6242ce18e743cb1f9a5fc51a2a44d8307739928add18
View on Chainz β†—

Height

#2,618,426

Difficulty

11.239534

Transactions

2

Size

835 B

Version

2

Bits

0b3d521c

Nonce

823,410,550

Timestamp

4/17/2018, 7:23:47 PM

Confirmations

4,211,983

Mined by

⛏️ P2SHAWMUdiny6L87KhSAutRpNDnium4h4Q5AYW

Merkle Root

55f328f6ae9e2983749f20046ab101a2090179993c9a68a8dfc2c7f09d6799d0
Transactions (2)
Coinbasec2665d4d3ac3e1…73aa86c7505dfc
1 in β†’ 1 out7.9100 XPM109 B
AWMUdiny…4h4Q5AYW
de872261e7617f…9ceb7910c30559
4 in β†’ 1 out14.9800 XPM636 B
AVhZLH6y…ceiE7RYq
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.

1.146 Γ— 10⁹⁡(96-digit number)
11466846921207994591…31298867681283614719
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
1.146 Γ— 10⁹⁡(96-digit number)
11466846921207994591…31298867681283614719
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.146 Γ— 10⁹⁡(96-digit number)
11466846921207994591…31298867681283614721
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
2.293 Γ— 10⁹⁡(96-digit number)
22933693842415989183…62597735362567229439
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.293 Γ— 10⁹⁡(96-digit number)
22933693842415989183…62597735362567229441
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
4.586 Γ— 10⁹⁡(96-digit number)
45867387684831978366…25195470725134458879
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.586 Γ— 10⁹⁡(96-digit number)
45867387684831978366…25195470725134458881
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
9.173 Γ— 10⁹⁡(96-digit number)
91734775369663956733…50390941450268917759
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.173 Γ— 10⁹⁡(96-digit number)
91734775369663956733…50390941450268917761
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
1.834 Γ— 10⁹⁢(97-digit number)
18346955073932791346…00781882900537835519
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.834 Γ— 10⁹⁢(97-digit number)
18346955073932791346…00781882900537835521
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
3.669 Γ— 10⁹⁢(97-digit number)
36693910147865582693…01563765801075671039
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:57,887,512 XPMΒ·at block #6,830,408 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