Block #246,124

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/5/2013, 9:51:58 PM · Difficulty 9.9643 · 6,564,978 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ff5afd133151a477da12e43846cf2436ff50a60bb7496733064d8ed71a3cd29c

View on Chainz ↗

Height

#246,124

Difficulty

9.964346

Transactions

Size

2.24 KB

Version

Bits

09f6df62

Nonce

1,059

Timestamp

11/5/2013, 9:51:58 PM

Confirmations

6,564,978

Mined by

⛏️ lRyh|ALd5yTY2V1TpjhCtBduYkduB11vgfAFVPZ

Merkle Root

5639f8f9fa032c2ce5f229c384af342a5a725e1096483d270a79f0f96fa8d9be

Transactions (1)

Coinbase5639f8f9fa032c…79f0f96fa8d9be

1 in → 63 out10.0300 XPM2.15 KB

ALd5yTY2…vgfAFVPZ ANuKx9Ke…wm7nrBRq ARpndEmc…Hg792kEk AMbCuLHZ…WSoStwkc AeNjg8HA…9AkdpcSC

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.

7.287 × 10⁹⁵(96-digit number)

72872749717829739909…67960304763010168319

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

7.287 × 10⁹⁵(96-digit number)

72872749717829739909…67960304763010168319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.287 × 10⁹⁵(96-digit number)

72872749717829739909…67960304763010168321

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

1.457 × 10⁹⁶(97-digit number)

14574549943565947981…35920609526020336639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.457 × 10⁹⁶(97-digit number)

14574549943565947981…35920609526020336641

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

2.914 × 10⁹⁶(97-digit number)

29149099887131895963…71841219052040673279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.914 × 10⁹⁶(97-digit number)

29149099887131895963…71841219052040673281

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

5.829 × 10⁹⁶(97-digit number)

58298199774263791927…43682438104081346559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.829 × 10⁹⁶(97-digit number)

58298199774263791927…43682438104081346561

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

1.165 × 10⁹⁷(98-digit number)

11659639954852758385…87364876208162693119

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 #246,124

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