XPM Prime Explorer symbol
XPMPrime Explorer

Block #1,612,066

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/3/2016, 7:22:47 AM Β· Difficulty 10.6040 Β· 5,230,157 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
fa6751408f0a5e1f41008bee0a0aed2b93231c30dea514275d2d2e8f8864668e
View on Chainz β†—

Height

#1,612,066

Difficulty

10.604032

Transactions

1

Size

199 B

Version

2

Bits

0a9aa1df

Nonce

1,550,612,039

Timestamp

6/3/2016, 7:22:47 AM

Confirmations

5,230,157

Mined by

⛏️ P2SHAFsA7Ukymy1P2VozZsNQzzLkvLS8TnUSWL

Merkle Root

e3954b8f0975b24ad7eabb305f698c726f1370eb0fa4d7abb369e8ddf9324324
Transactions (1)
Coinbasee3954b8f0975b2…69e8ddf9324324
1 in β†’ 1 out8.8800 XPM109 B
AFsA7Uky…S8TnUSWL
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.

4.276 Γ— 10⁹⁴(95-digit number)
42762271755275897913…43597087792798955519
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
4.276 Γ— 10⁹⁴(95-digit number)
42762271755275897913…43597087792798955519
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.276 Γ— 10⁹⁴(95-digit number)
42762271755275897913…43597087792798955521
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
8.552 Γ— 10⁹⁴(95-digit number)
85524543510551795827…87194175585597911039
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.552 Γ— 10⁹⁴(95-digit number)
85524543510551795827…87194175585597911041
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
1.710 Γ— 10⁹⁡(96-digit number)
17104908702110359165…74388351171195822079
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.710 Γ— 10⁹⁡(96-digit number)
17104908702110359165…74388351171195822081
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
3.420 Γ— 10⁹⁡(96-digit number)
34209817404220718331…48776702342391644159
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.420 Γ— 10⁹⁡(96-digit number)
34209817404220718331…48776702342391644161
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
6.841 Γ— 10⁹⁡(96-digit number)
68419634808441436662…97553404684783288319
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.841 Γ— 10⁹⁡(96-digit number)
68419634808441436662…97553404684783288321
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:57,982,182 XPMΒ·at block #6,842,222 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