XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,030,230

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 3/19/2017, 11:46:12 PM Β· Difficulty 10.6960 Β· 4,813,810 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
42f0b23c9de9f74273e2f76e6209babbd7048c9dc1549e46a7680b83a2936fd5
View on Chainz β†—

Height

#2,030,230

Difficulty

10.696011

Transactions

2

Size

390 B

Version

2

Bits

0ab22dcc

Nonce

497,114,551

Timestamp

3/19/2017, 11:46:12 PM

Confirmations

4,813,810

Mined by

⛏️ P2SHAVSNkkpNhkioK37zmJk985Z6FmHf8qfc3K

Merkle Root

3e04502b61ef6c8aebeb4e47106f9413085b2f18c406fdc0feddfc98a874f698
Transactions (2)
Coinbasea4995539119d8e…678138f76033da
1 in β†’ 1 out8.7400 XPM109 B
AVSNkkpN…Hf8qfc3K
32a88d552b83d5…e3c10c607cac7a
1 in β†’ 1 out19.7900 XPM191 B
ARsuhVkc…w3M6D8DV
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.

2.906 Γ— 10⁹⁴(95-digit number)
29062614627541376237…66671984307631971839
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
2.906 Γ— 10⁹⁴(95-digit number)
29062614627541376237…66671984307631971839
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.906 Γ— 10⁹⁴(95-digit number)
29062614627541376237…66671984307631971841
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
5.812 Γ— 10⁹⁴(95-digit number)
58125229255082752474…33343968615263943679
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.812 Γ— 10⁹⁴(95-digit number)
58125229255082752474…33343968615263943681
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
1.162 Γ— 10⁹⁡(96-digit number)
11625045851016550494…66687937230527887359
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.162 Γ— 10⁹⁡(96-digit number)
11625045851016550494…66687937230527887361
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
2.325 Γ— 10⁹⁡(96-digit number)
23250091702033100989…33375874461055774719
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.325 Γ— 10⁹⁡(96-digit number)
23250091702033100989…33375874461055774721
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
4.650 Γ— 10⁹⁡(96-digit number)
46500183404066201979…66751748922111549439
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.650 Γ— 10⁹⁡(96-digit number)
46500183404066201979…66751748922111549441
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:57,996,689 XPMΒ·at block #6,844,039 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