XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,233,769

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/2/2017, 1:09:02 PM Β· Difficulty 10.9461 Β· 4,603,081 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
8183855d516becffc73ec9a9271a4c9502d22fb47df6a4c0a914f6cb207910f0
View on Chainz β†—

Height

#2,233,769

Difficulty

10.946110

Transactions

1

Size

201 B

Version

2

Bits

0af23443

Nonce

340,268,235

Timestamp

8/2/2017, 1:09:02 PM

Confirmations

4,603,081

Mined by

⛏️ P2SHAaB79NBM1fbyTAsGJvMjRnkTmC9URJcPMd

Merkle Root

a68e6bdaa981c4e3d92519833e689d7668f644f7c387f8b34fe6d83335641470
Transactions (1)
Coinbasea68e6bdaa981c4…e6d83335641470
1 in β†’ 1 out8.3300 XPM110 B
AaB79NBM…9URJcPMd
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.

1.045 Γ— 10⁹⁸(99-digit number)
10450475298957373711…96608494861711851519
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
1.045 Γ— 10⁹⁸(99-digit number)
10450475298957373711…96608494861711851519
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.045 Γ— 10⁹⁸(99-digit number)
10450475298957373711…96608494861711851521
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
2.090 Γ— 10⁹⁸(99-digit number)
20900950597914747423…93216989723423703039
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.090 Γ— 10⁹⁸(99-digit number)
20900950597914747423…93216989723423703041
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
4.180 Γ— 10⁹⁸(99-digit number)
41801901195829494847…86433979446847406079
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.180 Γ— 10⁹⁸(99-digit number)
41801901195829494847…86433979446847406081
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
8.360 Γ— 10⁹⁸(99-digit number)
83603802391658989694…72867958893694812159
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.360 Γ— 10⁹⁸(99-digit number)
83603802391658989694…72867958893694812161
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
1.672 Γ— 10⁹⁹(100-digit number)
16720760478331797938…45735917787389624319
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.672 Γ— 10⁹⁹(100-digit number)
16720760478331797938…45735917787389624321
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
3.344 Γ— 10⁹⁹(100-digit number)
33441520956663595877…91471835574779248639
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:57,939,087 XPMΒ·at block #6,836,849 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