Block #1,386,471

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/26/2015, 9:08:43 PM · Difficulty 10.8146 · 5,439,030 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

81f79476296cec21f8c08cd48001a88f5ddc6555853c211449b3c0411da9c41e

View on Chainz ↗

Height

#1,386,471

Difficulty

10.814562

Transactions

Size

834 B

Version

Bits

0ad08723

Nonce

1,337,850,342

Timestamp

12/26/2015, 9:08:43 PM

Confirmations

5,439,030

Mined by

⛏️ P2SHAP7TABKJpaNER9EtprwudxjbAiPW65JPih

Merkle Root

befed17755123d479a8ddd24c3a043ad849a0e02cec1b08c8e084a27ed1c00bd

Transactions (2)

Coinbase24ca1346587dd9…a6f592334f9237

1 in → 1 out8.5500 XPM109 B

AP7TABKJ…PW65JPih

565b306c4d0415…14152c6bc0bc32

1 in → 14 out133.8550 XPM634 B

AG97kpGV…BGGHr9WA Aey6Apqa…TNhv4tQA AJCSxvYQ…F9fhZfUm AGGC96kT…tgntK4X9 ASG21nzq…iMYaGLq3

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.

7.525 × 10⁹⁷(98-digit number)

75256699955341686114…58335604804020797439

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

7.525 × 10⁹⁷(98-digit number)

75256699955341686114…58335604804020797439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.525 × 10⁹⁷(98-digit number)

75256699955341686114…58335604804020797441

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

1.505 × 10⁹⁸(99-digit number)

15051339991068337222…16671209608041594879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.505 × 10⁹⁸(99-digit number)

15051339991068337222…16671209608041594881

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

3.010 × 10⁹⁸(99-digit number)

30102679982136674445…33342419216083189759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.010 × 10⁹⁸(99-digit number)

30102679982136674445…33342419216083189761

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

6.020 × 10⁹⁸(99-digit number)

60205359964273348891…66684838432166379519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.020 × 10⁹⁸(99-digit number)

60205359964273348891…66684838432166379521

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

1.204 × 10⁹⁹(100-digit number)

12041071992854669778…33369676864332759039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.204 × 10⁹⁹(100-digit number)

12041071992854669778…33369676864332759041

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 #1,386,471

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