XPM Prime Explorer symbol
XPMPrime Explorer

Block #230,813

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/28/2013, 1:23:41 AM Β· Difficulty 9.9397 Β· 6,613,193 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
83731a3c3b0314c67c5ff0727ec1ab2721c3f72031098c7a3d6eafd32bade0aa
View on Chainz β†—

Height

#230,813

Difficulty

9.939710

Transactions

1

Size

198 B

Version

2

Bits

09f090da

Nonce

134,629

Timestamp

10/28/2013, 1:23:41 AM

Confirmations

6,613,193

Mined by

⛏️ P2SHAaNefT7q33Nms4wSPkKUDjKeMQm4v7SJ3s

Merkle Root

89b07fcf2210d31f737950684cc47f8a9462891ed216566430c4e9bc17dcb84f
Transactions (1)
Coinbase89b07fcf2210d3…c4e9bc17dcb84f
1 in β†’ 1 out10.1100 XPM109 B
AaNefT7q…m4v7SJ3s
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.

5.414 Γ— 10⁹¹(92-digit number)
54141100178339396912…43341154770558701799
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
5.414 Γ— 10⁹¹(92-digit number)
54141100178339396912…43341154770558701799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.414 Γ— 10⁹¹(92-digit number)
54141100178339396912…43341154770558701801
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
1.082 Γ— 10⁹²(93-digit number)
10828220035667879382…86682309541117403599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.082 Γ— 10⁹²(93-digit number)
10828220035667879382…86682309541117403601
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
2.165 Γ— 10⁹²(93-digit number)
21656440071335758765…73364619082234807199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.165 Γ— 10⁹²(93-digit number)
21656440071335758765…73364619082234807201
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
4.331 Γ— 10⁹²(93-digit number)
43312880142671517530…46729238164469614399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.331 Γ— 10⁹²(93-digit number)
43312880142671517530…46729238164469614401
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
8.662 Γ— 10⁹²(93-digit number)
86625760285343035060…93458476328939228799
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
8.662 Γ— 10⁹²(93-digit number)
86625760285343035060…93458476328939228801
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:57,996,429 XPMΒ·at block #6,844,005 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