XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,457,268

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 1/4/2018, 1:02:41 PM Β· Difficulty 10.9540 Β· 4,376,113 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b9cfcfa9dc7f27ef61aa51d03c0d7d35c5f3548ca5e40d480f239cc8dc9cd3c3
View on Chainz β†—

Height

#2,457,268

Difficulty

10.953995

Transactions

2

Size

391 B

Version

2

Bits

0af4390a

Nonce

386,811,463

Timestamp

1/4/2018, 1:02:41 PM

Confirmations

4,376,113

Mined by

⛏️ P2SHAJiF9hbTgfPn9dhbzirZwVgtASQR4phZ9U

Merkle Root

cb6d96f412adb1ca79c463b6dc96b03e0a6ce3be4010917c00e0624cbfa8bc30
Transactions (2)
Coinbaseec04a2d5fa798d…44d51cc0ab5ebc
1 in β†’ 1 out8.3300 XPM110 B
AJiF9hbT…QR4phZ9U
d9fa6ebc9fc7e3…e705191926b36e
1 in β†’ 1 out9.9900 XPM191 B
AXnR1v9S…9GHhMW69
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.

3.071 Γ— 10⁹⁡(96-digit number)
30714908393952136335…39530027781956654079
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
3.071 Γ— 10⁹⁡(96-digit number)
30714908393952136335…39530027781956654079
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.071 Γ— 10⁹⁡(96-digit number)
30714908393952136335…39530027781956654081
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
6.142 Γ— 10⁹⁡(96-digit number)
61429816787904272670…79060055563913308159
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.142 Γ— 10⁹⁡(96-digit number)
61429816787904272670…79060055563913308161
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
1.228 Γ— 10⁹⁢(97-digit number)
12285963357580854534…58120111127826616319
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.228 Γ— 10⁹⁢(97-digit number)
12285963357580854534…58120111127826616321
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
2.457 Γ— 10⁹⁢(97-digit number)
24571926715161709068…16240222255653232639
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.457 Γ— 10⁹⁢(97-digit number)
24571926715161709068…16240222255653232641
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
4.914 Γ— 10⁹⁢(97-digit number)
49143853430323418136…32480444511306465279
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.914 Γ— 10⁹⁢(97-digit number)
49143853430323418136…32480444511306465281
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
9.828 Γ— 10⁹⁢(97-digit number)
98287706860646836272…64960889022612930559
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:57,911,246 XPMΒ·at block #6,833,380 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