Block #1,067,492

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/20/2015, 6:31:21 AM · Difficulty 10.7398 · 5,749,430 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1ac23a4551c563ab084b62e3b902830491a9e2aec4b51522b2b47303e4b332f0

View on Chainz ↗

Height

#1,067,492

Difficulty

10.739835

Transactions

Size

1.15 KB

Version

Bits

0abd65d5

Nonce

753,900,824

Timestamp

5/20/2015, 6:31:21 AM

Confirmations

5,749,430

Mined by

⛏️ P2SHANxuXGDqc2KqYzQaBGA21ZQyAexsLGaY2c

Merkle Root

948cc94b242766e68dda8f2a9fe28da998012f68a19f41b85d71e50b24070ade

Transactions (4)

Coinbase94a7c10929bdb0…f134af4fc97730

1 in → 1 out8.6900 XPM109 B

ANxuXGDq…xsLGaY2c

4168a2618a7640…b537bfbcdcc682

1 in → 2 out8.6600 XPM226 B

AKXRtnSQ…zYPjCa9S AabjGLXP…e1SbqyrB

a5bcaf388dcf68…9ed4805885b8bf

3 in → 2 out10.4388 XPM523 B

AZXoCoEN…7AhxNjx1 AGkAjqVf…2zHcyRZP

000cfdd2822cff…432e4c5727cff6

1 in → 2 out5.0383 XPM225 B

AWg7Wpk8…YUvTj3gf Ae7YXEyn…hnSYZsCr

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.

1.037 × 10⁹⁴(95-digit number)

10379144637273186620…81869867588484693809

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

1.037 × 10⁹⁴(95-digit number)

10379144637273186620…81869867588484693809

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.037 × 10⁹⁴(95-digit number)

10379144637273186620…81869867588484693811

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

2.075 × 10⁹⁴(95-digit number)

20758289274546373240…63739735176969387619

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.075 × 10⁹⁴(95-digit number)

20758289274546373240…63739735176969387621

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

4.151 × 10⁹⁴(95-digit number)

41516578549092746481…27479470353938775239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.151 × 10⁹⁴(95-digit number)

41516578549092746481…27479470353938775241

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

8.303 × 10⁹⁴(95-digit number)

83033157098185492962…54958940707877550479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.303 × 10⁹⁴(95-digit number)

83033157098185492962…54958940707877550481

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

1.660 × 10⁹⁵(96-digit number)

16606631419637098592…09917881415755100959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.660 × 10⁹⁵(96-digit number)

16606631419637098592…09917881415755100961

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 #1,067,492

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