Block #248,462

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/7/2013, 9:52:07 AM · Difficulty 9.9657 · 6,562,217 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

897ab338a2958bb9f46f7538b678f5e8e3796fd6a6d503ef20a7ecee137d1bbe

View on Chainz ↗

Height

#248,462

Difficulty

9.965694

Transactions

Size

718 B

Version

Bits

09f737be

Nonce

6,026

Timestamp

11/7/2013, 9:52:07 AM

Confirmations

6,562,217

Mined by

⛏️ P2SHAMagrqHiNLcMvtRCPRKmUuBjNjxHGjQ4iF

Merkle Root

07df0d29872fc6852d4a03603ebb47606308283b14cc6a9e0757cc34e831dae0

Transactions (2)

Coinbasef4d284911e5bb6…290c718c9642c9

1 in → 1 out10.0600 XPM109 B

AMagrqHi…xHGjQ4iF

0b0c0ed23285e1…ff40ba529845a4

3 in → 2 out200.0104 XPM520 B

ALADBzoA…UX3rRXrS AQHTFGV2…j5Yzkftt

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.

2.480 × 10⁹³(94-digit number)

24803286351391088634…56308011270621532759

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

2.480 × 10⁹³(94-digit number)

24803286351391088634…56308011270621532759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.480 × 10⁹³(94-digit number)

24803286351391088634…56308011270621532761

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

4.960 × 10⁹³(94-digit number)

49606572702782177268…12616022541243065519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.960 × 10⁹³(94-digit number)

49606572702782177268…12616022541243065521

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

9.921 × 10⁹³(94-digit number)

99213145405564354537…25232045082486131039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.921 × 10⁹³(94-digit number)

99213145405564354537…25232045082486131041

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

1.984 × 10⁹⁴(95-digit number)

19842629081112870907…50464090164972262079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.984 × 10⁹⁴(95-digit number)

19842629081112870907…50464090164972262081

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

3.968 × 10⁹⁴(95-digit number)

39685258162225741814…00928180329944524159

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 #248,462

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