Block #280,057

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/28/2013, 1:36:51 PM · Difficulty 9.9735 · 6,529,797 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

307ef2c06beed72128c969c695ba87cc05d32514dbf8b3278df27556193e2fc8

View on Chainz ↗

Height

#280,057

Difficulty

9.973492

Transactions

Size

1.08 KB

Version

Bits

09f936c0

Nonce

163,708

Timestamp

11/28/2013, 1:36:51 PM

Confirmations

6,529,797

Mined by

⛏️ EaRFAZWiC56xr4FNeLHcLNFbmQbZQSNwextJca

Merkle Root

a233a01bea3a152c72fb6b5b83d08ee4d19117c2e7a7598fb400979961dedfba

Transactions (1)

Coinbasea233a01bea3a15…00979961dedfba

1 in → 28 out10.0200 XPM1015 B

AZWiC56x…NwextJca AUW89vJd…BiczGLRw AWwEQ3rx…wfDCHdhb AYRNBPg5…3q2SvNy5 AHutLKdv…GSZKPf4L

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.

2.843 × 10⁹⁴(95-digit number)

28439754670437763251…78936532721555166719

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

2.843 × 10⁹⁴(95-digit number)

28439754670437763251…78936532721555166719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.843 × 10⁹⁴(95-digit number)

28439754670437763251…78936532721555166721

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

5.687 × 10⁹⁴(95-digit number)

56879509340875526503…57873065443110333439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.687 × 10⁹⁴(95-digit number)

56879509340875526503…57873065443110333441

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

1.137 × 10⁹⁵(96-digit number)

11375901868175105300…15746130886220666879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.137 × 10⁹⁵(96-digit number)

11375901868175105300…15746130886220666881

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

2.275 × 10⁹⁵(96-digit number)

22751803736350210601…31492261772441333759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.275 × 10⁹⁵(96-digit number)

22751803736350210601…31492261772441333761

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

4.550 × 10⁹⁵(96-digit number)

45503607472700421202…62984523544882667519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.550 × 10⁹⁵(96-digit number)

45503607472700421202…62984523544882667521

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 #280,057

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