XPM Prime Explorer symbol
XPMPrime Explorer

Block #1,125,468

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/24/2015, 9:19:01 PM Β· Difficulty 10.9318 Β· 5,690,952 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
155d982e9d887857f5b4528174a14aed45d691437b819e3538f9a247a3563c83
View on Chainz β†—

Height

#1,125,468

Difficulty

10.931824

Transactions

2

Size

869 B

Version

2

Bits

0aee8c03

Nonce

700,903,223

Timestamp

6/24/2015, 9:19:01 PM

Confirmations

5,690,952

Mined by

⛏️ P2SHANeYxcjVfSknkCauHGAUUrTfYJ4JvQTUzn

Merkle Root

370b52f5983b514b3e31de8ddc702d790587ba796ff26808d75386ece6d1fe26
Transactions (2)
Coinbase34b32cc79c665b…837f6a21d41b64
1 in β†’ 1 out8.3600 XPM110 B
ANeYxcjV…4JvQTUzn
f91d0af149fdcc…39bf4da3173411
4 in β†’ 2 out10.1584 XPM669 B
AK9LxQQh…h24pctRmANCPVRU6…Sh1z3EUX
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.

2.364 Γ— 10⁹⁴(95-digit number)
23646104287130604268…08798221618088114719
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
2.364 Γ— 10⁹⁴(95-digit number)
23646104287130604268…08798221618088114719
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.364 Γ— 10⁹⁴(95-digit number)
23646104287130604268…08798221618088114721
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
4.729 Γ— 10⁹⁴(95-digit number)
47292208574261208536…17596443236176229439
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.729 Γ— 10⁹⁴(95-digit number)
47292208574261208536…17596443236176229441
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
9.458 Γ— 10⁹⁴(95-digit number)
94584417148522417072…35192886472352458879
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.458 Γ— 10⁹⁴(95-digit number)
94584417148522417072…35192886472352458881
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
1.891 Γ— 10⁹⁡(96-digit number)
18916883429704483414…70385772944704917759
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.891 Γ— 10⁹⁡(96-digit number)
18916883429704483414…70385772944704917761
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
3.783 Γ— 10⁹⁡(96-digit number)
37833766859408966829…40771545889409835519
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.783 Γ— 10⁹⁡(96-digit number)
37833766859408966829…40771545889409835521
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:57,775,487 XPMΒ·at block #6,816,419 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