Block #1,433,297

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/28/2016, 6:02:30 PM · Difficulty 10.7964 · 5,403,804 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7d6114841efe1d61c561cb97bdd5e9848e42b18a9537919fd037d14a4d5307f0

View on Chainz ↗

Height

#1,433,297

Difficulty

10.796446

Transactions

Size

937 B

Version

Bits

0acbe3e2

Nonce

16,743,631

Timestamp

1/28/2016, 6:02:30 PM

Confirmations

5,403,804

Mined by

⛏️ P2SHAdU1DRpbJ81QSSDQpUJfWZLSTbRn4KAPaW

Merkle Root

1e7d5e13986c991d9a60cc32c198865b2d42066ada6151142f43a8891a064327

Transactions (2)

Coinbase12896ab08b3aa5…8ea7ae7fe439ff

1 in → 1 out8.5800 XPM110 B

AdU1DRpb…Rn4KAPaW

c295288317804c…11cb773ba39061

1 in → 17 out169.5546 XPM736 B

APBczLAZ…6gbiQXmJ AKJWP64b…xFn4ggkM AaePbnhk…XyJe37ND AdGCRGgf…hgWkQYT1 AdzvYMJi…DDea9q7x

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.

8.857 × 10⁹⁶(97-digit number)

88579717299332875858…74923417058948321279

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

8.857 × 10⁹⁶(97-digit number)

88579717299332875858…74923417058948321279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.857 × 10⁹⁶(97-digit number)

88579717299332875858…74923417058948321281

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

1.771 × 10⁹⁷(98-digit number)

17715943459866575171…49846834117896642559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.771 × 10⁹⁷(98-digit number)

17715943459866575171…49846834117896642561

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

3.543 × 10⁹⁷(98-digit number)

35431886919733150343…99693668235793285119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.543 × 10⁹⁷(98-digit number)

35431886919733150343…99693668235793285121

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

7.086 × 10⁹⁷(98-digit number)

70863773839466300686…99387336471586570239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.086 × 10⁹⁷(98-digit number)

70863773839466300686…99387336471586570241

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

1.417 × 10⁹⁸(99-digit number)

14172754767893260137…98774672943173140479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.417 × 10⁹⁸(99-digit number)

14172754767893260137…98774672943173140481

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 #1,433,297

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