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Block #2,023,428

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 3/15/2017, 2:38:46 AM Β· Difficulty 10.7092 Β· 4,814,678 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b06f6b20c67413ad0c105f548e12c02b4712a8f4af806bb9fe2cc5b985e606c3
View on Chainz β†—

Height

#2,023,428

Difficulty

10.709242

Transactions

2

Size

836 B

Version

2

Bits

0ab590da

Nonce

1,402,448,160

Timestamp

3/15/2017, 2:38:46 AM

Confirmations

4,814,678

Mined by

⛏️ P2SHAPMZM9P8MuXREL33W1Yx4Ak7y4czoLEyrd

Merkle Root

1a4ecf60585042f32813185dde477bb39f2e30e8ebe76d6e6c392700bba98b52
Transactions (2)
Coinbase57948c5843ef14…6d42d7bafbdf19
1 in β†’ 1 out8.7200 XPM109 B
APMZM9P8…czoLEyrd
65e1c52043d210…fdc7b26118df9b
4 in β†’ 1 out653.8800 XPM637 B
AXZHNZXb…cRmdyo3Z
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.

5.060 Γ— 10⁹³(94-digit number)
50602455745861522480…14180108170175996259
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
5.060 Γ— 10⁹³(94-digit number)
50602455745861522480…14180108170175996259
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.060 Γ— 10⁹³(94-digit number)
50602455745861522480…14180108170175996261
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
1.012 Γ— 10⁹⁴(95-digit number)
10120491149172304496…28360216340351992519
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.012 Γ— 10⁹⁴(95-digit number)
10120491149172304496…28360216340351992521
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
2.024 Γ— 10⁹⁴(95-digit number)
20240982298344608992…56720432680703985039
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.024 Γ— 10⁹⁴(95-digit number)
20240982298344608992…56720432680703985041
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
4.048 Γ— 10⁹⁴(95-digit number)
40481964596689217984…13440865361407970079
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.048 Γ— 10⁹⁴(95-digit number)
40481964596689217984…13440865361407970081
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
8.096 Γ— 10⁹⁴(95-digit number)
80963929193378435969…26881730722815940159
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
8.096 Γ— 10⁹⁴(95-digit number)
80963929193378435969…26881730722815940161
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:57,949,202 XPMΒ·at block #6,838,105 Β· updates every 60s
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