Block #2,639,688

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 4/30/2018, 6:00:20 PM · Difficulty 11.5486 · 4,202,642 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9fea6f08a66cd828baa0b13d8711d4b49bf4bea32da56340469e32fa39bb27f4

View on Chainz ↗

Height

#2,639,688

Difficulty

11.548613

Transactions

Size

1.46 KB

Version

Bits

0b8c71eb

Nonce

463,157,375

Timestamp

4/30/2018, 6:00:20 PM

Confirmations

4,202,642

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

f23472ee436a3d3a5e0c55eefac8b1e367017aa17c68ab8ee3e8748f532d8c3f

Transactions (2)

Coinbase4c9027a402cc23…5e70611b9b5de4

1 in → 1 out7.5100 XPM110 B

Adqah8zh…1WwoHJ9t

9acb3d86db8d43…4f0a620f59adcf

8 in → 3 out28.2103 XPM1.26 KB

ASk9H3sY…qUG8r1d4 AHmoHaoV…guxDRZ3w AdUoToES…K4thUFdv

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.

2.048 × 10⁹⁸(99-digit number)

20487287710114530112…50941154298099998719

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

2.048 × 10⁹⁸(99-digit number)

20487287710114530112…50941154298099998719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.048 × 10⁹⁸(99-digit number)

20487287710114530112…50941154298099998721

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

4.097 × 10⁹⁸(99-digit number)

40974575420229060225…01882308596199997439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.097 × 10⁹⁸(99-digit number)

40974575420229060225…01882308596199997441

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

8.194 × 10⁹⁸(99-digit number)

81949150840458120451…03764617192399994879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.194 × 10⁹⁸(99-digit number)

81949150840458120451…03764617192399994881

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

1.638 × 10⁹⁹(100-digit number)

16389830168091624090…07529234384799989759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.638 × 10⁹⁹(100-digit number)

16389830168091624090…07529234384799989761

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

3.277 × 10⁹⁹(100-digit number)

32779660336183248180…15058468769599979519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.277 × 10⁹⁹(100-digit number)

32779660336183248180…15058468769599979521

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

6.555 × 10⁹⁹(100-digit number)

65559320672366496361…30116937539199959039

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #2,639,688

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