XPM Prime Explorer symbol
XPMPrime Explorer

Block #223,834

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/23/2013, 8:12:02 AM Β· Difficulty 9.9373 Β· 6,571,138 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
48bd945e340c78ac1c5b147a39d3902bbf4c29105e411ae2f82bda410258ef59
View on Chainz β†—

Height

#223,834

Difficulty

9.937327

Transactions

2

Size

425 B

Version

2

Bits

09eff4b0

Nonce

155,173

Timestamp

10/23/2013, 8:12:02 AM

Confirmations

6,571,138

Mined by

⛏️ P2SHAe9sxfkUNU9aFwrqjcsKBNuEt8rpDKfT31

Merkle Root

29a9dc1fcfd13216f9b25c18414097157fe28fa4dad7775cff4a2ae87a5f405e
Transactions (2)
Coinbasefe1bb0e2448734…63b134161c58c9
1 in β†’ 1 out10.1200 XPM109 B
Ae9sxfkU…rpDKfT31
9c6deaf69ab23c…1d1ac77d1e4362
1 in β†’ 2 out2.1254 XPM226 B
AJMdpogz…9ekXcAJ4ANUPa5nC…gS5uF4Pm
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.

3.050 Γ— 10⁹⁴(95-digit number)
30504422233221658976…06022034131384806399
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
3.050 Γ— 10⁹⁴(95-digit number)
30504422233221658976…06022034131384806399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.050 Γ— 10⁹⁴(95-digit number)
30504422233221658976…06022034131384806401
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
6.100 Γ— 10⁹⁴(95-digit number)
61008844466443317953…12044068262769612799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.100 Γ— 10⁹⁴(95-digit number)
61008844466443317953…12044068262769612801
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
1.220 Γ— 10⁹⁡(96-digit number)
12201768893288663590…24088136525539225599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.220 Γ— 10⁹⁡(96-digit number)
12201768893288663590…24088136525539225601
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
2.440 Γ— 10⁹⁡(96-digit number)
24403537786577327181…48176273051078451199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.440 Γ— 10⁹⁡(96-digit number)
24403537786577327181…48176273051078451201
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
4.880 Γ— 10⁹⁡(96-digit number)
48807075573154654362…96352546102156902399
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,603,815 XPMΒ·at block #6,794,971 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.
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK