Block #281,060

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/28/2013, 9:37:45 PM · Difficulty 9.9761 · 6,525,682 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

218d287efaac818cdc84c8c456ce85d564ca6b22871bc084f707736f8a63293b

View on Chainz ↗

Height

#281,060

Difficulty

9.976126

Transactions

Size

1.11 KB

Version

Bits

09f9e364

Nonce

9,502

Timestamp

11/28/2013, 9:37:45 PM

Confirmations

6,525,682

Mined by

⛏️ IaR=AbtgNzNbw1hJh3uoaBwXxdpmiY9Atvu81w

Merkle Root

72ea53a32732821c5ee3e0e607a0a3de4d51284b3f171cfe99834c11719ba587

Transactions (1)

Coinbase72ea53a3273282…834c11719ba587

1 in → 29 out10.0100 XPM1.02 KB

AbtgNzNb…9Atvu81w AH4k3yjN…PUFV6WdB Ae58nAEb…GFUA15fv Ae2pnFaX…7SPtJMsm ANkX1YyE…kHwVW1hd

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.

3.580 × 10⁹⁴(95-digit number)

35802345721570943736…16525398832915071359

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

3.580 × 10⁹⁴(95-digit number)

35802345721570943736…16525398832915071359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.580 × 10⁹⁴(95-digit number)

35802345721570943736…16525398832915071361

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

7.160 × 10⁹⁴(95-digit number)

71604691443141887473…33050797665830142719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.160 × 10⁹⁴(95-digit number)

71604691443141887473…33050797665830142721

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

1.432 × 10⁹⁵(96-digit number)

14320938288628377494…66101595331660285439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.432 × 10⁹⁵(96-digit number)

14320938288628377494…66101595331660285441

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

2.864 × 10⁹⁵(96-digit number)

28641876577256754989…32203190663320570879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.864 × 10⁹⁵(96-digit number)

28641876577256754989…32203190663320570881

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

5.728 × 10⁹⁵(96-digit number)

57283753154513509978…64406381326641141759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.728 × 10⁹⁵(96-digit number)

57283753154513509978…64406381326641141761

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #281,060

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