Block #1,434,031

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/29/2016, 3:04:43 AM · Difficulty 10.8041 · 5,404,384 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d96533b04033f8dab5632817cd2d9c93b1341200d740acc95353a54ee9d2b910

View on Chainz ↗

Height

#1,434,031

Difficulty

10.804093

Transactions

Size

697 B

Version

Bits

0acdd90c

Nonce

706,003,274

Timestamp

1/29/2016, 3:04:43 AM

Confirmations

5,404,384

Mined by

⛏️ P2SHAJGQWpqfiFRc2b88VYWfYvjV3S8vfs3yHY

Merkle Root

8259327ee8615340f3334fa3c0809a3c1df1275f8617060c34fe0b3c4ed8e496

Transactions (2)

Coinbasea67e1e03826498…ffa863b2747ec5

1 in → 1 out8.5600 XPM109 B

AJGQWpqf…8vfs3yHY

849ffa121b54d7…416037cf344f07

1 in → 10 out163.7675 XPM498 B

AHbZrwFG…6daMnsDr ARB6qyYM…UfzKMJj1 AP2LUbiQ…pzQH2E6D AKJWP64b…xFn4ggkM AVjBizVs…tVDrfWHQ

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.

1.467 × 10⁹⁴(95-digit number)

14675539154957148337…50653652509485776959

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

1.467 × 10⁹⁴(95-digit number)

14675539154957148337…50653652509485776959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.467 × 10⁹⁴(95-digit number)

14675539154957148337…50653652509485776961

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

2.935 × 10⁹⁴(95-digit number)

29351078309914296675…01307305018971553919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.935 × 10⁹⁴(95-digit number)

29351078309914296675…01307305018971553921

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

5.870 × 10⁹⁴(95-digit number)

58702156619828593351…02614610037943107839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.870 × 10⁹⁴(95-digit number)

58702156619828593351…02614610037943107841

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

1.174 × 10⁹⁵(96-digit number)

11740431323965718670…05229220075886215679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.174 × 10⁹⁵(96-digit number)

11740431323965718670…05229220075886215681

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

2.348 × 10⁹⁵(96-digit number)

23480862647931437340…10458440151772431359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.348 × 10⁹⁵(96-digit number)

23480862647931437340…10458440151772431361

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 #1,434,031

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