XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,118,695

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/16/2017, 6:50:45 AM Β· Difficulty 10.9091 Β· 4,719,533 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
9571ef609cb5575cc6c32a910c06102e8b2b36df32f5c9b2f10f9c95cf412c86
View on Chainz β†—

Height

#2,118,695

Difficulty

10.909149

Transactions

2

Size

1.97 KB

Version

2

Bits

0ae8bdfa

Nonce

537,785,519

Timestamp

5/16/2017, 6:50:45 AM

Confirmations

4,719,533

Mined by

⛏️ P2SHAPZy1ZqKM7zQzGM8ytzLpeePcH6F8f7Ejj

Merkle Root

8c84847e6b1145941fe084b3a2cf38d7561e14c3adbcaa0f9237888576bfdefd
Transactions (2)
Coinbasecbba10e1d8a343…dfc81e9dd077f5
1 in β†’ 1 out8.4300 XPM109 B
APZy1ZqK…6F8f7Ejj
0d6921edb64558…82ab2c30e129c1
12 in β†’ 1 out1995.7393 XPM1.77 KB
AQZVhvkQ…55MyFfM2
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.

1.996 Γ— 10⁹⁡(96-digit number)
19960406025391319101…95133888996677075199
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
1.996 Γ— 10⁹⁡(96-digit number)
19960406025391319101…95133888996677075199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.996 Γ— 10⁹⁡(96-digit number)
19960406025391319101…95133888996677075201
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
3.992 Γ— 10⁹⁡(96-digit number)
39920812050782638202…90267777993354150399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.992 Γ— 10⁹⁡(96-digit number)
39920812050782638202…90267777993354150401
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
7.984 Γ— 10⁹⁡(96-digit number)
79841624101565276404…80535555986708300799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.984 Γ— 10⁹⁡(96-digit number)
79841624101565276404…80535555986708300801
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
1.596 Γ— 10⁹⁢(97-digit number)
15968324820313055280…61071111973416601599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.596 Γ— 10⁹⁢(97-digit number)
15968324820313055280…61071111973416601601
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
3.193 Γ— 10⁹⁢(97-digit number)
31936649640626110561…22142223946833203199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.193 Γ— 10⁹⁢(97-digit number)
31936649640626110561…22142223946833203201
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
6.387 Γ— 10⁹⁢(97-digit number)
63873299281252221123…44284447893666406399
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:57,950,100 XPMΒ·at block #6,838,227 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