Block #248,631

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/7/2013, 12:13:35 PM · Difficulty 9.9659 · 6,548,225 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1f29a90084f0d693d6c868d9dbf67445a9c2b3901cddbb4728d64099ecf528f9

View on Chainz ↗

Height

#248,631

Difficulty

9.965889

Transactions

Size

2.26 KB

Version

Bits

09f74488

Nonce

65,033

Timestamp

11/7/2013, 12:13:35 PM

Confirmations

6,548,225

Mined by

⛏️ 7R{AJaGRnajU4FKPNSjrHvpAByLABiCHGoy6E

Merkle Root

399a40b54656c49fabefe88343953a36ff541013562330cb82b34e412c1768fa

Transactions (2)

Coinbasefd5cf26ca49755…ccb0b2aa44b7f4

1 in → 57 out10.0300 XPM1.95 KB

AJaGRnaj…iCHGoy6E ANuKx9Ke…wm7nrBRq ARpndEmc…Hg792kEk AMbCuLHZ…WSoStwkc AKDTDDtx…iqvw9cdY

17f686e1070a2b…cfda25b6c841ff

1 in → 2 out10.0500 XPM225 B

ASgpbzGy…9QJ1F2XL AeXSKXyB…3LVeYMHt

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.

1.224 × 10⁹⁵(96-digit number)

12242395932930745348…48634975896952995829

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

1.224 × 10⁹⁵(96-digit number)

12242395932930745348…48634975896952995829

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.224 × 10⁹⁵(96-digit number)

12242395932930745348…48634975896952995831

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

2.448 × 10⁹⁵(96-digit number)

24484791865861490696…97269951793905991659

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.448 × 10⁹⁵(96-digit number)

24484791865861490696…97269951793905991661

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

4.896 × 10⁹⁵(96-digit number)

48969583731722981393…94539903587811983319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.896 × 10⁹⁵(96-digit number)

48969583731722981393…94539903587811983321

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

9.793 × 10⁹⁵(96-digit number)

97939167463445962786…89079807175623966639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.793 × 10⁹⁵(96-digit number)

97939167463445962786…89079807175623966641

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

1.958 × 10⁹⁶(97-digit number)

19587833492689192557…78159614351247933279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.958 × 10⁹⁶(97-digit number)

19587833492689192557…78159614351247933281

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