Block #548,289

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/16/2014, 10:30:43 PM · Difficulty 10.9589 · 6,247,881 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

fd18534c92ac06e0f695c483fc5beb6db0dcf50a129e1f0943211d4d01db1c53

View on Chainz ↗

Height

#548,289

Difficulty

10.958861

Transactions

Size

1.66 KB

Version

Bits

0af577ee

Nonce

154,624,435

Timestamp

5/16/2014, 10:30:43 PM

Confirmations

6,247,881

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

72103de3750385315de7ece0ddecc54a9a0f57c902b5c5e51389edaae242a2f1

Transactions (5)

Coinbase9b4fe56b0d6f27…8aa22067e9ca78

1 in → 1 out8.3500 XPM116 B

ANSXnLY2…Sd25TjkD

a2be7ecb7b73fd…a30cfea253e1df

1 in → 2 out5.5960 XPM226 B

AGdWVjRk…LFVsqCnK AQBTKpmR…AeZreXwd

a89e036f8d1305…7538146230f221

1 in → 2 out5.4225 XPM227 B

AFvXyDeW…4QQrCTPJ AdzyUmyH…S7U2CE5g

adba85dc1984da…c73030e6be999d

2 in → 2 out5.2058 XPM374 B

AYc4orSE…sS9VLYBT ANCUoayq…dKNUHmxo

6858027849ee9d…c6791290d68a32

4 in → 2 out2.0134 XPM668 B

AKvBdrg4…hsMyU7xU AJPSj4aY…V9S9Bt73

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.

1.662 × 10⁹⁹(100-digit number)

16620811028195766489…80561182827630225279

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

1.662 × 10⁹⁹(100-digit number)

16620811028195766489…80561182827630225279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.662 × 10⁹⁹(100-digit number)

16620811028195766489…80561182827630225281

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

3.324 × 10⁹⁹(100-digit number)

33241622056391532978…61122365655260450559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.324 × 10⁹⁹(100-digit number)

33241622056391532978…61122365655260450561

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

6.648 × 10⁹⁹(100-digit number)

66483244112783065956…22244731310520901119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.648 × 10⁹⁹(100-digit number)

66483244112783065956…22244731310520901121

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

1.329 × 10¹⁰⁰(101-digit number)

13296648822556613191…44489462621041802239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.329 × 10¹⁰⁰(101-digit number)

13296648822556613191…44489462621041802241

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

2.659 × 10¹⁰⁰(101-digit number)

26593297645113226382…88978925242083604479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.659 × 10¹⁰⁰(101-digit number)

26593297645113226382…88978925242083604481

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