Block #1,347,549

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/29/2015, 2:35:33 PM · Difficulty 10.8255 · 5,460,589 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

71664919c043e2fd6f13c5222e5183e1d700acbc8b57a132bf798332ea0272c6

View on Chainz ↗

Height

#1,347,549

Difficulty

10.825468

Transactions

Size

5.73 KB

Version

Bits

0ad351e4

Nonce

172,031,381

Timestamp

11/29/2015, 2:35:33 PM

Confirmations

5,460,589

Mined by

⛏️ P2SHAGd4kSBWA5nHRnV4tm5fp8oMrbHLMYLjbk

Merkle Root

f13797330a2e4be4363ecc31185aa6a56b9402162ca057afed274c4415d2bb34

Transactions (2)

Coinbaseb396a48065d870…a27af521f9c717

1 in → 1 out8.5800 XPM109 B

AGd4kSBW…HLMYLjbk

7e188b576a59a2…cb885bb446ee25

38 in → 1 out43.8429 XPM5.54 KB

AYeGLxtJ…3XFCDFMm

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.

1.076 × 10⁹⁶(97-digit number)

10762999844095961484…06963325892128737279

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

1.076 × 10⁹⁶(97-digit number)

10762999844095961484…06963325892128737279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.076 × 10⁹⁶(97-digit number)

10762999844095961484…06963325892128737281

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

2.152 × 10⁹⁶(97-digit number)

21525999688191922968…13926651784257474559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.152 × 10⁹⁶(97-digit number)

21525999688191922968…13926651784257474561

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

4.305 × 10⁹⁶(97-digit number)

43051999376383845936…27853303568514949119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.305 × 10⁹⁶(97-digit number)

43051999376383845936…27853303568514949121

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

8.610 × 10⁹⁶(97-digit number)

86103998752767691872…55706607137029898239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.610 × 10⁹⁶(97-digit number)

86103998752767691872…55706607137029898241

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

1.722 × 10⁹⁷(98-digit number)

17220799750553538374…11413214274059796479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.722 × 10⁹⁷(98-digit number)

17220799750553538374…11413214274059796481

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 #1,347,549

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