XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,829,525

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/8/2018, 1:28:23 AM Β· Difficulty 11.7133 Β· 4,014,977 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
6fdba70ecab0d392ac957c91a1ce35ad76e18635e5ddbfdeebe1f11768a5b016
View on Chainz β†—

Height

#2,829,525

Difficulty

11.713340

Transactions

2

Size

575 B

Version

2

Bits

0bb69d75

Nonce

1,865,393,472

Timestamp

9/8/2018, 1:28:23 AM

Confirmations

4,014,977

Mined by

⛏️ P2SHAGAo1gULBdLWJnDHJc5GZ3SjB2BhVyYsPQ

Merkle Root

787e5bdcca59f0e0571b8bc5484227671d7ad9f38e91e2a5e4c3e7b6d7c1e232
Transactions (2)
Coinbase53de7151b6ab00…7358845231e3a9
1 in β†’ 1 out7.2900 XPM110 B
AGAo1gUL…BhVyYsPQ
6840780748618e…92495fb763045a
2 in β†’ 2 out182.3022 XPM375 B
AaCt2Z2e…QB2Doko7AMWDTU6w…21BSF3qD
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.

1.488 Γ— 10⁹⁴(95-digit number)
14883665327679418184…90205225730591096319
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
1.488 Γ— 10⁹⁴(95-digit number)
14883665327679418184…90205225730591096319
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.488 Γ— 10⁹⁴(95-digit number)
14883665327679418184…90205225730591096321
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
2.976 Γ— 10⁹⁴(95-digit number)
29767330655358836368…80410451461182192639
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.976 Γ— 10⁹⁴(95-digit number)
29767330655358836368…80410451461182192641
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
5.953 Γ— 10⁹⁴(95-digit number)
59534661310717672737…60820902922364385279
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.953 Γ— 10⁹⁴(95-digit number)
59534661310717672737…60820902922364385281
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
1.190 Γ— 10⁹⁡(96-digit number)
11906932262143534547…21641805844728770559
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.190 Γ— 10⁹⁡(96-digit number)
11906932262143534547…21641805844728770561
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
2.381 Γ— 10⁹⁡(96-digit number)
23813864524287069094…43283611689457541119
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.381 Γ— 10⁹⁡(96-digit number)
23813864524287069094…43283611689457541121
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
4.762 Γ— 10⁹⁡(96-digit number)
47627729048574138189…86567223378915082239
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:58,000,413 XPMΒ·at block #6,844,501 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