XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,051,545

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/3/2017, 1:31:32 PM Β· Difficulty 10.7174 Β· 4,787,644 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
1a3c22dd64e71adde929725e2320ee0e24134e7d5d0bd5d372b973fd352873e3
View on Chainz β†—

Height

#2,051,545

Difficulty

10.717412

Transactions

1

Size

200 B

Version

2

Bits

0ab7a857

Nonce

45,702,655

Timestamp

4/3/2017, 1:31:32 PM

Confirmations

4,787,644

Mined by

⛏️ P2SHAZeDcq1qHTcgpVSHFEZCx78dXszJ9pGac6

Merkle Root

f04a7ae9ed900c2c32879be722ea121b82207c2fd04a646f6d0d838bc2caca3a
Transactions (1)
Coinbasef04a7ae9ed900c…0d838bc2caca3a
1 in β†’ 1 out8.6900 XPM110 B
AZeDcq1q…zJ9pGac6
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.

2.292 Γ— 10⁹⁡(96-digit number)
22927860291512738068…91542538265590046439
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
2.292 Γ— 10⁹⁡(96-digit number)
22927860291512738068…91542538265590046439
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.292 Γ— 10⁹⁡(96-digit number)
22927860291512738068…91542538265590046441
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
4.585 Γ— 10⁹⁡(96-digit number)
45855720583025476136…83085076531180092879
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.585 Γ— 10⁹⁡(96-digit number)
45855720583025476136…83085076531180092881
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
9.171 Γ— 10⁹⁡(96-digit number)
91711441166050952273…66170153062360185759
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.171 Γ— 10⁹⁡(96-digit number)
91711441166050952273…66170153062360185761
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
1.834 Γ— 10⁹⁢(97-digit number)
18342288233210190454…32340306124720371519
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.834 Γ— 10⁹⁢(97-digit number)
18342288233210190454…32340306124720371521
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
3.668 Γ— 10⁹⁢(97-digit number)
36684576466420380909…64680612249440743039
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.668 Γ— 10⁹⁢(97-digit number)
36684576466420380909…64680612249440743041
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:57,957,789 XPMΒ·at block #6,839,188 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