Block #1,077,382

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/26/2015, 9:16:37 PM · Difficulty 10.7583 · 5,749,339 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

56db6ce97d6edcae71aca4cd958cc92afd649ac910a45f758e82166240c30ff6

View on Chainz ↗

Height

#1,077,382

Difficulty

10.758307

Transactions

Size

2.05 KB

Version

Bits

0ac22069

Nonce

249,342,226

Timestamp

5/26/2015, 9:16:37 PM

Confirmations

5,749,339

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

33855c91d35afaad761cda95b6fcef602d661fe9172e8cd1bacf7477f32f59c0

Transactions (2)

Coinbaseb35f10f1464f3e…4cd8cea34b990a

1 in → 1 out8.6500 XPM116 B

ANSXnLY2…Sd25TjkD

c3f74d1d92e431…00e3ebd90ea56f

1 in → 51 out87.8614 XPM1.85 KB

AejcsRHy…X15pK4mH AGrojGJ2…agp341GG AWqGS9Ba…EgCxqg66 AHiVFmS7…SSWQafCc ALQG96NK…5zPi39NB

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

4.307 × 10⁹⁵(96-digit number)

43079097243845937597…39582597746370176639

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × 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 — Twin Prime Pair (origin ± 1)

origin − 1

4.307 × 10⁹⁵(96-digit number)

43079097243845937597…39582597746370176639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.307 × 10⁹⁵(96-digit number)

43079097243845937597…39582597746370176641

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

8.615 × 10⁹⁵(96-digit number)

86158194487691875195…79165195492740353279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.615 × 10⁹⁵(96-digit number)

86158194487691875195…79165195492740353281

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

1.723 × 10⁹⁶(97-digit number)

17231638897538375039…58330390985480706559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.723 × 10⁹⁶(97-digit number)

17231638897538375039…58330390985480706561

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

3.446 × 10⁹⁶(97-digit number)

34463277795076750078…16660781970961413119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.446 × 10⁹⁶(97-digit number)

34463277795076750078…16660781970961413121

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

6.892 × 10⁹⁶(97-digit number)

68926555590153500156…33321563941922826239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.892 × 10⁹⁶(97-digit number)

68926555590153500156…33321563941922826241

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

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 — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★☆☆☆

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 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — 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 − 1 and p+2 = origin/primorial + 1

Cross-reference on Chainz Explorer

Block #1,077,382

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