XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,160,481

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/14/2017, 3:08:00 PM Β· Difficulty 10.9016 Β· 4,649,475 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
35a9df41fd948ec4aef580258d7a30f7ec09cbc226d32b2c2d65e4fa777b26b2
View on Chainz β†—

Height

#2,160,481

Difficulty

10.901569

Transactions

2

Size

6.75 KB

Version

2

Bits

0ae6cd32

Nonce

68,637,377

Timestamp

6/14/2017, 3:08:00 PM

Confirmations

4,649,475

Mined by

⛏️ P2SHAYrvN6toSgerZyZtDZPzQPX3nweXNFnayC

Merkle Root

b568bdd8c01560aebd81f90788ac1f14a0bd928ad5f863906cafe1786b1db0c4
Transactions (2)
Coinbasec65d366df38d6e…8a4cb2d31286f1
1 in β†’ 1 out8.4800 XPM109 B
AYrvN6to…eXNFnayC
0ffe4266743488…550db4a5f64605
45 in β†’ 1 out553.7820 XPM6.55 KB
AZjr24ws…v8TZvuZv
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.

2.211 Γ— 10⁹⁴(95-digit number)
22116747871316566770…33008967564108387679
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
2.211 Γ— 10⁹⁴(95-digit number)
22116747871316566770…33008967564108387679
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.211 Γ— 10⁹⁴(95-digit number)
22116747871316566770…33008967564108387681
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
4.423 Γ— 10⁹⁴(95-digit number)
44233495742633133541…66017935128216775359
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.423 Γ— 10⁹⁴(95-digit number)
44233495742633133541…66017935128216775361
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
8.846 Γ— 10⁹⁴(95-digit number)
88466991485266267082…32035870256433550719
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.846 Γ— 10⁹⁴(95-digit number)
88466991485266267082…32035870256433550721
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
1.769 Γ— 10⁹⁡(96-digit number)
17693398297053253416…64071740512867101439
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.769 Γ— 10⁹⁡(96-digit number)
17693398297053253416…64071740512867101441
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
3.538 Γ— 10⁹⁡(96-digit number)
35386796594106506832…28143481025734202879
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.538 Γ— 10⁹⁡(96-digit number)
35386796594106506832…28143481025734202881
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:57,723,730 XPMΒ·at block #6,809,955 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

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