Block #248,681

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/7/2013, 12:47:50 PM · Difficulty 9.9660 · 6,592,257 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

96a996e2468e42d3fa4bcfd8b8db38988ee2b2430a0122f96c25888337f02172

View on Chainz ↗

Height

#248,681

Difficulty

9.965995

Transactions

Size

2.11 KB

Version

Bits

09f74b6e

Nonce

3,808

Timestamp

11/7/2013, 12:47:50 PM

Confirmations

6,592,257

Mined by

⛏️ P2SHAeL7UAFbYJxtsFPY1Wp7S8F2EUW9mPDyGL

Merkle Root

02b49271692a3d654c10d589492274e3c33e8b906d6678c3b077e6c49b0b8bd0

Transactions (3)

Coinbase98e11fe46dfbed…7ad962d6947157

1 in → 2 out10.0800 XPM137 B

AeL7UAFb…W9mPDyGL Abiw8n3q…ZnZfgvQW

92efafccf4666a…56c84370a9c76f

10 in → 2 out9.9145 XPM1.52 KB

ATncW3cD…19QSP2rG AH1YAuGj…zTku1UGb

eba994eb3bca4a…bcd5e96ddae22f

2 in → 2 out2.6559 XPM376 B

ALHNHJYj…SntQ8iPV AQpRzzDz…PeodSkXe

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.

5.756 × 10⁹⁸(99-digit number)

57561327204446345526…07479511926348828029

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

5.756 × 10⁹⁸(99-digit number)

57561327204446345526…07479511926348828029

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.756 × 10⁹⁸(99-digit number)

57561327204446345526…07479511926348828031

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

1.151 × 10⁹⁹(100-digit number)

11512265440889269105…14959023852697656059

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.151 × 10⁹⁹(100-digit number)

11512265440889269105…14959023852697656061

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

2.302 × 10⁹⁹(100-digit number)

23024530881778538210…29918047705395312119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.302 × 10⁹⁹(100-digit number)

23024530881778538210…29918047705395312121

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

4.604 × 10⁹⁹(100-digit number)

46049061763557076420…59836095410790624239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.604 × 10⁹⁹(100-digit number)

46049061763557076420…59836095410790624241

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

9.209 × 10⁹⁹(100-digit number)

92098123527114152841…19672190821581248479

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 #248,681

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