XPM Prime Explorer symbol
XPMPrime Explorer

Block #3,505,487

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/8/2020, 4:17:30 PM Β· Difficulty 10.9302 Β· 3,337,098 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
5584156c26e0a11282b4e64f3a135bdffd1738cc632a61cbe30a2ee1b798cf1d
View on Chainz β†—

Height

#3,505,487

Difficulty

10.930242

Transactions

2

Size

7.47 KB

Version

2

Bits

0aee2458

Nonce

72,760,650

Timestamp

1/8/2020, 4:17:30 PM

Confirmations

3,337,098

Mined by

⛏️ P2SHASiq2qtKTzQ7sbERFE8Jp8HjsgVMhmk7yL

Merkle Root

dce70734c792edc1248e6748906f25b5e9238f3136cce69972c41768bc2c824f
Transactions (2)
Coinbase3f1aa7bbab6a14…fcca1053323513
1 in β†’ 1 out8.4400 XPM110 B
ASiq2qtK…VMhmk7yL
989f5100c47d61…c925d10a8451dd
50 in β†’ 1 out199.9200 XPM7.27 KB
ALcTQaSP…1C5Yf2Zi
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.

5.320 Γ— 10⁹³(94-digit number)
53206345236985641098…34312692197969395879
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
5.320 Γ— 10⁹³(94-digit number)
53206345236985641098…34312692197969395879
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.320 Γ— 10⁹³(94-digit number)
53206345236985641098…34312692197969395881
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
1.064 Γ— 10⁹⁴(95-digit number)
10641269047397128219…68625384395938791759
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.064 Γ— 10⁹⁴(95-digit number)
10641269047397128219…68625384395938791761
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
2.128 Γ— 10⁹⁴(95-digit number)
21282538094794256439…37250768791877583519
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.128 Γ— 10⁹⁴(95-digit number)
21282538094794256439…37250768791877583521
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
4.256 Γ— 10⁹⁴(95-digit number)
42565076189588512879…74501537583755167039
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.256 Γ— 10⁹⁴(95-digit number)
42565076189588512879…74501537583755167041
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
8.513 Γ— 10⁹⁴(95-digit number)
85130152379177025758…49003075167510334079
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
8.513 Γ— 10⁹⁴(95-digit number)
85130152379177025758…49003075167510334081
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:57,985,109 XPMΒ·at block #6,842,584 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