Block #247,758

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/6/2013, 11:19:22 PM · Difficulty 9.9652 · 6,560,690 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8e32022ef5ed352d372b4ce001eeb2e6f992f27614d443b46d7e4a61f629d24d

View on Chainz ↗

Height

#247,758

Difficulty

9.965184

Transactions

Size

2.01 KB

Version

Bits

09f71647

Nonce

92,243

Timestamp

11/6/2013, 11:19:22 PM

Confirmations

6,560,690

Mined by

⛏️ RzAL3P2QDvggde3uU26ZG8H2z2AzgbbaSnCj

Merkle Root

1f1fdcc25f5daf3b9f38d8527ae0c35db9243e9224a7ca767511ff20c808525b

Transactions (1)

Coinbase1f1fdcc25f5daf…11ff20c808525b

1 in → 56 out10.0300 XPM1.92 KB

AL3P2QDv…gbbaSnCj AQSKrTwi…FZPpP64p AReBFi8Q…Qq1cm1uS Ac5sZcdP…kzV4eckG ALzxhR4e…bD4bNcZe

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.

5.000 × 10¹⁰¹(102-digit number)

50005036216915082697…09423206829130634399

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

5.000 × 10¹⁰¹(102-digit number)

50005036216915082697…09423206829130634399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.000 × 10¹⁰¹(102-digit number)

50005036216915082697…09423206829130634401

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

1.000 × 10¹⁰²(103-digit number)

10001007243383016539…18846413658261268799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.000 × 10¹⁰²(103-digit number)

10001007243383016539…18846413658261268801

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

2.000 × 10¹⁰²(103-digit number)

20002014486766033079…37692827316522537599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.000 × 10¹⁰²(103-digit number)

20002014486766033079…37692827316522537601

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

4.000 × 10¹⁰²(103-digit number)

40004028973532066158…75385654633045075199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.000 × 10¹⁰²(103-digit number)

40004028973532066158…75385654633045075201

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

8.000 × 10¹⁰²(103-digit number)

80008057947064132316…50771309266090150399

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 #247,758

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