XPM Prime Explorer symbol
XPMPrime Explorer

Block #190,915

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/2/2013, 7:23:31 PM Β· Difficulty 9.8748 Β· 6,634,033 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
27f3bb5a56708c84784674ceb6f979c5b41bc42db576f14265320f2846855099
View on Chainz β†—

Height

#190,915

Difficulty

9.874800

Transactions

1

Size

200 B

Version

2

Bits

09dff2e1

Nonce

69,223

Timestamp

10/2/2013, 7:23:31 PM

Confirmations

6,634,033

Mined by

⛏️ P2SHASiN1vnGnb4VLXNU9Yym429CfsnPBYx4TC

Merkle Root

f72e2586ce0bb8dd6d151f504aed1c7cf16f3ce410d89ec5c4cfd9e6b21e86af
Transactions (1)
Coinbasef72e2586ce0bb8…cfd9e6b21e86af
1 in β†’ 1 out10.2400 XPM109 B
ASiN1vnG…nPBYx4TC
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.

4.195 Γ— 10⁹⁢(97-digit number)
41950551743614345868…40061639114843542399
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
4.195 Γ— 10⁹⁢(97-digit number)
41950551743614345868…40061639114843542399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.195 Γ— 10⁹⁢(97-digit number)
41950551743614345868…40061639114843542401
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
8.390 Γ— 10⁹⁢(97-digit number)
83901103487228691736…80123278229687084799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.390 Γ— 10⁹⁢(97-digit number)
83901103487228691736…80123278229687084801
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
1.678 Γ— 10⁹⁷(98-digit number)
16780220697445738347…60246556459374169599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.678 Γ— 10⁹⁷(98-digit number)
16780220697445738347…60246556459374169601
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
3.356 Γ— 10⁹⁷(98-digit number)
33560441394891476694…20493112918748339199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.356 Γ— 10⁹⁷(98-digit number)
33560441394891476694…20493112918748339201
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
6.712 Γ— 10⁹⁷(98-digit number)
67120882789782953389…40986225837496678399
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,843,662 XPMΒ·at block #6,824,947 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