XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,008,890

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 3/5/2017, 2:12:46 AM Β· Difficulty 10.7019 Β· 4,818,033 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
a7c3f91ceaf5f4dd3efa27e894b78a9e235d601f46ced44b258b6de9b47a5225
View on Chainz β†—

Height

#2,008,890

Difficulty

10.701859

Transactions

2

Size

459 B

Version

2

Bits

0ab3ad05

Nonce

601,536,857

Timestamp

3/5/2017, 2:12:46 AM

Confirmations

4,818,033

Mined by

⛏️ P2SHAHNYgvj5bGY7fG7PDuXRTp8uPAD8Hi1GUM

Merkle Root

06db2067fe8d415acb992609d19e9634cd24daf171dd1ed2148487a8e53f6974
Transactions (2)
Coinbasebb93ce70340fe4…ec4d95a806519e
1 in β†’ 1 out8.7300 XPM109 B
AHNYgvj5…D8Hi1GUM
d322c4e5612bd2…b0d02df82d9e08
1 in β†’ 3 out1.2400 XPM260 B
AXhp4JXB…QF94JBpdAR6qgsuL…x1tjMz93AKsebF9o…26T4a6vn
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.

1.635 Γ— 10⁹⁡(96-digit number)
16354134401915190719…04785526251679753279
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
1.635 Γ— 10⁹⁡(96-digit number)
16354134401915190719…04785526251679753279
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.635 Γ— 10⁹⁡(96-digit number)
16354134401915190719…04785526251679753281
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
3.270 Γ— 10⁹⁡(96-digit number)
32708268803830381438…09571052503359506559
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.270 Γ— 10⁹⁡(96-digit number)
32708268803830381438…09571052503359506561
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
6.541 Γ— 10⁹⁡(96-digit number)
65416537607660762876…19142105006719013119
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.541 Γ— 10⁹⁡(96-digit number)
65416537607660762876…19142105006719013121
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
1.308 Γ— 10⁹⁢(97-digit number)
13083307521532152575…38284210013438026239
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.308 Γ— 10⁹⁢(97-digit number)
13083307521532152575…38284210013438026241
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
2.616 Γ— 10⁹⁢(97-digit number)
26166615043064305150…76568420026876052479
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.616 Γ— 10⁹⁢(97-digit number)
26166615043064305150…76568420026876052481
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,859,555 XPMΒ·at block #6,826,922 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