XPM Prime Explorer symbol
XPMPrime Explorer

Block #3,046,822

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 2/10/2019, 10:14:22 AM Β· Difficulty 10.9961 Β· 3,798,507 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
dbb85b50ea52f4a20bfe4f356fa3b1b60c58faa58bdf28580c7cbfbf89fe09ac
View on Chainz β†—

Height

#3,046,822

Difficulty

10.996090

Transactions

1

Size

200 B

Version

2

Bits

0afeffc2

Nonce

527,726,341

Timestamp

2/10/2019, 10:14:22 AM

Confirmations

3,798,507

Mined by

⛏️ P2SHAUhjokokGBrQRx2CtHWNPSvbj6k5m93PZR

Merkle Root

a7b2a81fc98962842dbf03c220f0774131f82755590679a847146fea76608dc8
Transactions (1)
Coinbasea7b2a81fc98962…146fea76608dc8
1 in β†’ 1 out8.2600 XPM110 B
AUhjokok…k5m93PZR
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.

3.962 Γ— 10⁹⁡(96-digit number)
39625558102667528228…68081282632906135679
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
3.962 Γ— 10⁹⁡(96-digit number)
39625558102667528228…68081282632906135679
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.962 Γ— 10⁹⁡(96-digit number)
39625558102667528228…68081282632906135681
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
7.925 Γ— 10⁹⁡(96-digit number)
79251116205335056457…36162565265812271359
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.925 Γ— 10⁹⁡(96-digit number)
79251116205335056457…36162565265812271361
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
1.585 Γ— 10⁹⁢(97-digit number)
15850223241067011291…72325130531624542719
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.585 Γ— 10⁹⁢(97-digit number)
15850223241067011291…72325130531624542721
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
3.170 Γ— 10⁹⁢(97-digit number)
31700446482134022583…44650261063249085439
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.170 Γ— 10⁹⁢(97-digit number)
31700446482134022583…44650261063249085441
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
6.340 Γ— 10⁹⁢(97-digit number)
63400892964268045166…89300522126498170879
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.340 Γ— 10⁹⁢(97-digit number)
63400892964268045166…89300522126498170881
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
1.268 Γ— 10⁹⁷(98-digit number)
12680178592853609033…78601044252996341759
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:58,007,072 XPMΒ·at block #6,845,328 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