Block #2,458,502

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/5/2018, 8:37:52 AM · Difficulty 10.9545 · 4,381,282 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e5776cf412a6a40e566cb574b8e75e24904ae29260ba9a0bddb59542b71961b9

View on Chainz ↗

Height

#2,458,502

Difficulty

10.954531

Transactions

Size

427 B

Version

Bits

0af45c1e

Nonce

1,232,342,028

Timestamp

1/5/2018, 8:37:52 AM

Confirmations

4,381,282

Mined by

⛏️ P2SHAejJUUSCgQnpgEytb1y81Zh8qmf6HX9BoF

Merkle Root

26e013decd7e0cfd7d1315b18a269e74f9f0b8d85a7a5396823149d424aee168

Transactions (2)

Coinbasedb91907fe1b2d6…31f78c8b3ae193

1 in → 1 out8.3300 XPM110 B

AejJUUSC…f6HX9BoF

2d4c97b657e1f6…bf7b0f3bd5f1ad

1 in → 2 out981.5644 XPM225 B

AVD4e9yL…MykXNoLT AXwsmPPr…6VMrFrtM

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.

4.492 × 10⁹⁸(99-digit number)

44920609429578695812…95903023259503329279

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

4.492 × 10⁹⁸(99-digit number)

44920609429578695812…95903023259503329279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.492 × 10⁹⁸(99-digit number)

44920609429578695812…95903023259503329281

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

8.984 × 10⁹⁸(99-digit number)

89841218859157391625…91806046519006658559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.984 × 10⁹⁸(99-digit number)

89841218859157391625…91806046519006658561

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

1.796 × 10⁹⁹(100-digit number)

17968243771831478325…83612093038013317119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.796 × 10⁹⁹(100-digit number)

17968243771831478325…83612093038013317121

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

3.593 × 10⁹⁹(100-digit number)

35936487543662956650…67224186076026634239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.593 × 10⁹⁹(100-digit number)

35936487543662956650…67224186076026634241

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

7.187 × 10⁹⁹(100-digit number)

71872975087325913300…34448372152053268479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.187 × 10⁹⁹(100-digit number)

71872975087325913300…34448372152053268481

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 #2,458,502

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