Block #248,450

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/7/2013, 9:37:59 AM · Difficulty 9.9657 · 6,567,817 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6c84396deee9755154455e2c80da5c607100d7058c952cd8ecc24f1a93b21fdc

View on Chainz ↗

Height

#248,450

Difficulty

9.965712

Transactions

Size

902 B

Version

Bits

09f738ed

Nonce

4,358

Timestamp

11/7/2013, 9:37:59 AM

Confirmations

6,567,817

Mined by

⛏️ P2SHAKcbk49N7DP3nse7MJr3Ed6rZiGJbKa7j1

Merkle Root

0863e1c550954d82f5f7dab60787926cb160aa414eb46d42bec63e7ac693c74f

Transactions (2)

Coinbase2d0347c861bf2c…2844b81ae3b49a

1 in → 2 out10.0600 XPM141 B

AKcbk49N…GJbKa7j1 Abiw8n3q…ZnZfgvQW

4330f323b3be22…f7672141ab48e6

4 in → 2 out3.1293 XPM669 B

Acy5e2n9…qqd8ckvj AYrmzCck…Qx8iHzzJ

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.

3.115 × 10⁹⁸(99-digit number)

31156110797807032570…66432267663121663999

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

3.115 × 10⁹⁸(99-digit number)

31156110797807032570…66432267663121663999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.115 × 10⁹⁸(99-digit number)

31156110797807032570…66432267663121664001

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

6.231 × 10⁹⁸(99-digit number)

62312221595614065140…32864535326243327999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.231 × 10⁹⁸(99-digit number)

62312221595614065140…32864535326243328001

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

1.246 × 10⁹⁹(100-digit number)

12462444319122813028…65729070652486655999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.246 × 10⁹⁹(100-digit number)

12462444319122813028…65729070652486656001

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

2.492 × 10⁹⁹(100-digit number)

24924888638245626056…31458141304973311999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.492 × 10⁹⁹(100-digit number)

24924888638245626056…31458141304973312001

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

4.984 × 10⁹⁹(100-digit number)

49849777276491252112…62916282609946623999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.984 × 10⁹⁹(100-digit number)

49849777276491252112…62916282609946624001

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 #248,450

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