Block #494,068

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/15/2014, 11:56:38 PM · Difficulty 10.7125 · 6,313,118 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4f8ab63e7164e8d283de48267fb9b2d668b1102efad68b59a3aa84c07f2492de

View on Chainz ↗

Height

#494,068

Difficulty

10.712484

Transactions

Size

1.08 KB

Version

Bits

0ab66561

Nonce

477,084,185

Timestamp

4/15/2014, 11:56:38 PM

Confirmations

6,313,118

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

9ea475d3880699f5fe2ea5d90e69ae688ffe3db82f31ae39d4a8923c3f9e11c4

Transactions (5)

Coinbase4c166bb013ffb7…69715fca509ede

1 in → 1 out8.7400 XPM116 B

AbwWkWZt…kawDhufa

8deac09ff25b4c…a4f2465bac678c

1 in → 2 out8.7400 XPM225 B

AXnL68UR…jsxeGUhN AGXZsrsv…byWHmMFT

c06c5beb66be44…603f61f446d0c6

1 in → 2 out8.7400 XPM226 B

AbrQ6M5J…VtfaQ3gU Adxq4iBL…36hNMLjP

b493991cc7cd48…63a4e3d501f83d

1 in → 2 out8.7400 XPM226 B

ARENd3V6…66TeRsPd AZnPb1i4…aJnYZ49t

c417d3d8a475d8…419f4339d52f3b

1 in → 2 out8.7400 XPM226 B

AQvEzARN…VBvxuQym APQCLq5D…cpNbYpoy

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.

4.403 × 10⁹⁸(99-digit number)

44031719466501495105…66415889372558182399

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

4.403 × 10⁹⁸(99-digit number)

44031719466501495105…66415889372558182399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.403 × 10⁹⁸(99-digit number)

44031719466501495105…66415889372558182401

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

8.806 × 10⁹⁸(99-digit number)

88063438933002990211…32831778745116364799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.806 × 10⁹⁸(99-digit number)

88063438933002990211…32831778745116364801

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

1.761 × 10⁹⁹(100-digit number)

17612687786600598042…65663557490232729599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.761 × 10⁹⁹(100-digit number)

17612687786600598042…65663557490232729601

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

3.522 × 10⁹⁹(100-digit number)

35225375573201196084…31327114980465459199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.522 × 10⁹⁹(100-digit number)

35225375573201196084…31327114980465459201

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

7.045 × 10⁹⁹(100-digit number)

70450751146402392169…62654229960930918399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.045 × 10⁹⁹(100-digit number)

70450751146402392169…62654229960930918401

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 #494,068

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