XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,832,014

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/9/2018, 5:24:22 PM Β· Difficulty 11.7187 Β· 4,011,052 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
7584696cafa6b5dcc27102ba643b9815a238cdb1e50cb6cf1e18a1d7fece63b5
View on Chainz β†—

Height

#2,832,014

Difficulty

11.718656

Transactions

1

Size

201 B

Version

2

Bits

0bb7f9d6

Nonce

485,409,256

Timestamp

9/9/2018, 5:24:22 PM

Confirmations

4,011,052

Mined by

⛏️ P2SHAMrG2SJ2krCDoPBV33Mp6eQbQdkvuhECZm

Merkle Root

ccd1a1102760a868f0e77091be9876479e1c7350c7ff63bdc59defb5a960105b
Transactions (1)
Coinbaseccd1a1102760a8…9defb5a960105b
1 in β†’ 1 out7.2700 XPM110 B
AMrG2SJ2…kvuhECZm
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.

1.358 Γ— 10⁹⁢(97-digit number)
13586089150059456465…70132692703385495039
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
1.358 Γ— 10⁹⁢(97-digit number)
13586089150059456465…70132692703385495039
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.358 Γ— 10⁹⁢(97-digit number)
13586089150059456465…70132692703385495041
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
2.717 Γ— 10⁹⁢(97-digit number)
27172178300118912931…40265385406770990079
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.717 Γ— 10⁹⁢(97-digit number)
27172178300118912931…40265385406770990081
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
5.434 Γ— 10⁹⁢(97-digit number)
54344356600237825862…80530770813541980159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.434 Γ— 10⁹⁢(97-digit number)
54344356600237825862…80530770813541980161
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
1.086 Γ— 10⁹⁷(98-digit number)
10868871320047565172…61061541627083960319
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.086 Γ— 10⁹⁷(98-digit number)
10868871320047565172…61061541627083960321
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
2.173 Γ— 10⁹⁷(98-digit number)
21737742640095130345…22123083254167920639
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.173 Γ— 10⁹⁷(98-digit number)
21737742640095130345…22123083254167920641
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
4.347 Γ— 10⁹⁷(98-digit number)
43475485280190260690…44246166508335841279
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:57,988,886 XPMΒ·at block #6,843,065 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