Block #248,107

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/7/2013, 4:37:19 AM · Difficulty 9.9654 · 6,564,753 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8bd0d25a48719123637f4352ceefd8120fa9d0665a107e7ff8dcca4d2cf8ad04

View on Chainz ↗

Height

#248,107

Difficulty

9.965406

Transactions

Size

686 B

Version

Bits

09f724e1

Nonce

13,341

Timestamp

11/7/2013, 4:37:19 AM

Confirmations

6,564,753

Mined by

⛏️ P2SHAKcbk49N7DP3nse7MJr3Ed6rZiGJbKa7j1

Merkle Root

596e306c980d882dc5824976fc8058053117f25f3d614d2b78e3f60f57524bd8

Transactions (3)

Coinbase8544764b9b338c…828eac4f8ff0e4

1 in → 2 out10.0700 XPM142 B

AKcbk49N…GJbKa7j1 ASNt3cJa…L5zCqAYM

f64bb20883358f…cf3253a88d41c0

1 in → 2 out10.0500 XPM226 B

AaEqbxd7…uVpcsWqq AUT8exGA…7RCuiusE

e7d74f9ee482d1…c4584ceffba5c3

1 in → 2 out2.1882 XPM227 B

AYnWdFRw…6po8X7iA AP7Viti2…TJywVibJ

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.

1.114 × 10⁹⁸(99-digit number)

11146224809241012968…28362801082637431039

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

1.114 × 10⁹⁸(99-digit number)

11146224809241012968…28362801082637431039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.114 × 10⁹⁸(99-digit number)

11146224809241012968…28362801082637431041

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

2.229 × 10⁹⁸(99-digit number)

22292449618482025936…56725602165274862079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.229 × 10⁹⁸(99-digit number)

22292449618482025936…56725602165274862081

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

4.458 × 10⁹⁸(99-digit number)

44584899236964051873…13451204330549724159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.458 × 10⁹⁸(99-digit number)

44584899236964051873…13451204330549724161

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

8.916 × 10⁹⁸(99-digit number)

89169798473928103746…26902408661099448319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.916 × 10⁹⁸(99-digit number)

89169798473928103746…26902408661099448321

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

1.783 × 10⁹⁹(100-digit number)

17833959694785620749…53804817322198896639

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 #248,107

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