Block #273,398

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/25/2013, 6:57:28 PM · Difficulty 9.9548 · 6,536,511 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

97629c0708b6ad62b80819cb0f606a8a75e52ab0b73d24ae67dbf71a761f2c3b

View on Chainz ↗

Height

#273,398

Difficulty

9.954760

Transactions

Size

1.11 KB

Version

Bits

09f46b28

Nonce

29,461

Timestamp

11/25/2013, 6:57:28 PM

Confirmations

6,536,511

Mined by

⛏️ +aRAAPt2Q6LmHLHtfvcoCE7kDPydWSRy2ethJx

Merkle Root

1caea1a7c60d134ddc2e0f6fb9b23a8f4d4448503e44f93ea85b0350e7ac2ddd

Transactions (2)

Coinbase9aa8e1b8beffa6…d1b6943a9ea343

1 in → 18 out10.0800 XPM675 B

APt2Q6Lm…Ry2ethJx AGPBDvpY…HsUDJ9oq ASPzomex…JkjSwA1z APvpz12N…NjdsxTYA AGfgeL1m…sELT7P7c

1a3a42f2f46f9a…60fb3cc8adac43

2 in → 2 out275.9031 XPM373 B

AcuayjUK…6mfc4Qhp AMvDEhZv…V5YvJTWj

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.

2.199 × 10⁹²(93-digit number)

21997945734693051334…99357952516647289599

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

2.199 × 10⁹²(93-digit number)

21997945734693051334…99357952516647289599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.199 × 10⁹²(93-digit number)

21997945734693051334…99357952516647289601

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

4.399 × 10⁹²(93-digit number)

43995891469386102668…98715905033294579199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.399 × 10⁹²(93-digit number)

43995891469386102668…98715905033294579201

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

8.799 × 10⁹²(93-digit number)

87991782938772205336…97431810066589158399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.799 × 10⁹²(93-digit number)

87991782938772205336…97431810066589158401

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

1.759 × 10⁹³(94-digit number)

17598356587754441067…94863620133178316799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.759 × 10⁹³(94-digit number)

17598356587754441067…94863620133178316801

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

3.519 × 10⁹³(94-digit number)

35196713175508882134…89727240266356633599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.519 × 10⁹³(94-digit number)

35196713175508882134…89727240266356633601

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 #273,398

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