Block #251,514

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/9/2013, 1:52:22 AM · Difficulty 9.9700 · 6,553,529 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1f9c102497a46c15506d0b0f50ca058aabf25f27599618869d4011f33aa5dc83

View on Chainz ↗

Height

#251,514

Difficulty

9.969960

Transactions

Size

1.71 KB

Version

Bits

09f84f47

Nonce

422,236

Timestamp

11/9/2013, 1:52:22 AM

Confirmations

6,553,529

Mined by

⛏️ zaR}ARskhKebzwhUsQms8dTj78qtmaUgDvvX9P

Merkle Root

ae004b4ab3c525af73f47bd34a2643d554a81dd41275ecd75c35c3a0466038d4

Transactions (1)

Coinbaseae004b4ab3c525…35c3a0466038d4

1 in → 47 out10.0300 XPM1.62 KB

ARskhKeb…UgDvvX9P AKXeSXzu…yeuNjvhB AQtzUSwq…htAuF3yC ALFWpHxd…zhX7LjhL AKDTDDtx…iqvw9cdY

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.

1.292 × 10⁹⁵(96-digit number)

12929011946724110348…09377435438680022399

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

1.292 × 10⁹⁵(96-digit number)

12929011946724110348…09377435438680022399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.292 × 10⁹⁵(96-digit number)

12929011946724110348…09377435438680022401

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

2.585 × 10⁹⁵(96-digit number)

25858023893448220696…18754870877360044799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.585 × 10⁹⁵(96-digit number)

25858023893448220696…18754870877360044801

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

5.171 × 10⁹⁵(96-digit number)

51716047786896441393…37509741754720089599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.171 × 10⁹⁵(96-digit number)

51716047786896441393…37509741754720089601

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

1.034 × 10⁹⁶(97-digit number)

10343209557379288278…75019483509440179199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.034 × 10⁹⁶(97-digit number)

10343209557379288278…75019483509440179201

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

2.068 × 10⁹⁶(97-digit number)

20686419114758576557…50038967018880358399

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