XPM Prime Explorer symbol
XPMPrime Explorer

Block #1,534,610

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/10/2016, 8:48:28 AM Β· Difficulty 10.6174 Β· 5,281,983 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
7a98f17abe391f12cc64fa1370f872c8f96e0c652df42c80a9a9e06f109b9dc1
View on Chainz β†—

Height

#1,534,610

Difficulty

10.617398

Transactions

2

Size

7.61 KB

Version

2

Bits

0a9e0dc6

Nonce

581,855,571

Timestamp

4/10/2016, 8:48:28 AM

Confirmations

5,281,983

Mined by

⛏️ P2SHAGMwt4XdUC2P8DwqFPBszHxk5xdhrruwjC

Merkle Root

b494b21e5507d87022b7b11d4f160f217b55793ee7fb3f20b7ec375366b7eec7
Transactions (2)
Coinbase0da1f4a0d79741…b9b8029e085b8c
1 in β†’ 1 out8.9400 XPM109 B
AGMwt4Xd…dhrruwjC
a2f21deacc0825…d32e83871f491e
51 in β†’ 1 out1243.6057 XPM7.42 KB
ARuucgaS…78i2Uuf4
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.

2.048 Γ— 10⁹⁡(96-digit number)
20483467341325150662…51363785012303051999
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
2.048 Γ— 10⁹⁡(96-digit number)
20483467341325150662…51363785012303051999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.048 Γ— 10⁹⁡(96-digit number)
20483467341325150662…51363785012303052001
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
4.096 Γ— 10⁹⁡(96-digit number)
40966934682650301324…02727570024606103999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.096 Γ— 10⁹⁡(96-digit number)
40966934682650301324…02727570024606104001
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
8.193 Γ— 10⁹⁡(96-digit number)
81933869365300602649…05455140049212207999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.193 Γ— 10⁹⁡(96-digit number)
81933869365300602649…05455140049212208001
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
1.638 Γ— 10⁹⁢(97-digit number)
16386773873060120529…10910280098424415999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.638 Γ— 10⁹⁢(97-digit number)
16386773873060120529…10910280098424416001
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
3.277 Γ— 10⁹⁢(97-digit number)
32773547746120241059…21820560196848831999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.277 Γ— 10⁹⁢(97-digit number)
32773547746120241059…21820560196848832001
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:57,776,868 XPMΒ·at block #6,816,592 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