Block #2,670,254

TWNLength 12★★★★☆

Bi-Twin Chain · Discovered 5/20/2018, 6:25:46 PM · Difficulty 11.6815 · 4,162,330 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

fc98ce249ff85f348ca859ef6f7dad9a06b0b787d014ccec0e9c4d6ec33316fc

View on Chainz ↗

Height

#2,670,254

Difficulty

11.681462

Transactions

Size

507 B

Version

Bits

0bae7443

Nonce

23,467,234

Timestamp

5/20/2018, 6:25:46 PM

Confirmations

4,162,330

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

c4fed9649607c1e46d91b3bd97066e41f6bff1197581d9d9bc185514e60734df

Transactions (2)

Coinbase6040e48acffc75…ec8aede8d39331

1 in → 1 out7.3300 XPM110 B

Adqah8zh…1WwoHJ9t

09bd42dc5a80a8…f1e5ad8001b9a7

2 in → 2 out14.6500 XPM306 B

Aei7Ymdr…MjKXcgCp AQFJVoPs…TQvnQYCJ

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.

6.293 × 10⁹⁵(96-digit number)

62930456040670014216…53794062078740559359

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

6.293 × 10⁹⁵(96-digit number)

62930456040670014216…53794062078740559359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.293 × 10⁹⁵(96-digit number)

62930456040670014216…53794062078740559361

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

1.258 × 10⁹⁶(97-digit number)

12586091208134002843…07588124157481118719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.258 × 10⁹⁶(97-digit number)

12586091208134002843…07588124157481118721

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

2.517 × 10⁹⁶(97-digit number)

25172182416268005686…15176248314962237439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.517 × 10⁹⁶(97-digit number)

25172182416268005686…15176248314962237441

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

5.034 × 10⁹⁶(97-digit number)

50344364832536011373…30352496629924474879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.034 × 10⁹⁶(97-digit number)

50344364832536011373…30352496629924474881

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

1.006 × 10⁹⁷(98-digit number)

10068872966507202274…60704993259848949759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.006 × 10⁹⁷(98-digit number)

10068872966507202274…60704993259848949761

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

2.013 × 10⁹⁷(98-digit number)

20137745933014404549…21409986519697899519

Verify on FactorDB ↗Wolfram Alpha ↗

2^5 × origin + 1

2.013 × 10⁹⁷(98-digit number)

20137745933014404549…21409986519697899521

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^5 × origin + 1 − 2^5 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 12 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

ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

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 #2,670,254

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