Block #252,001

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/9/2013, 8:18:45 AM · Difficulty 9.9706 · 6,558,674 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f8106013ca28506f4f47b9890686943be0d37c0f3a56a4a691cf78f28f55702d

View on Chainz ↗

Height

#252,001

Difficulty

9.970575

Transactions

Size

1.18 KB

Version

Bits

09f8779b

Nonce

16,669

Timestamp

11/9/2013, 8:18:45 AM

Confirmations

6,558,674

Mined by

⛏️ P2SHAZDUEbdSvp8cw8AAZ1fERZUqSYRYKMRZET

Merkle Root

d9bafa222f27db5768f2da77959340534e8b0ed4a03797f4c5432b90cf01f8da

Transactions (5)

Coinbasee879ccfac5ae27…61ee73a2fabee8

1 in → 2 out10.0800 XPM137 B

AZDUEbdS…RYKMRZET AKNbfPoc…jfkpwAyL

33ea43d730165f…24964f823ffa50

1 in → 1 out10.0600 XPM157 B

AJRwGPSP…QDRWdi2B

074d697715b66d…bee16e1433f3f5

1 in → 2 out10.0400 XPM225 B

AeWXBmrk…fxQGr3Xj AX4m4qRb…B7FY18Mn

9ca8ea92b713ce…4795abb25ca700

1 in → 2 out8.0290 XPM225 B

Aa7zV3sb…uVWrGDSx AaVFHFSq…bCnX1Bpw

f8276a54fb10d5…f9cfa457e20b8a

2 in → 2 out4.5409 XPM373 B

AcAzoFRQ…1B8Wttdg Abw8D7Bc…EioKVM91

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.

4.550 × 10⁹⁶(97-digit number)

45508096879150676286…10230284302930122239

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

4.550 × 10⁹⁶(97-digit number)

45508096879150676286…10230284302930122239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.550 × 10⁹⁶(97-digit number)

45508096879150676286…10230284302930122241

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

9.101 × 10⁹⁶(97-digit number)

91016193758301352573…20460568605860244479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.101 × 10⁹⁶(97-digit number)

91016193758301352573…20460568605860244481

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

1.820 × 10⁹⁷(98-digit number)

18203238751660270514…40921137211720488959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.820 × 10⁹⁷(98-digit number)

18203238751660270514…40921137211720488961

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

3.640 × 10⁹⁷(98-digit number)

36406477503320541029…81842274423440977919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.640 × 10⁹⁷(98-digit number)

36406477503320541029…81842274423440977921

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

7.281 × 10⁹⁷(98-digit number)

72812955006641082058…63684548846881955839

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 #252,001

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