Block #271,036

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/24/2013, 9:16:44 AM · Difficulty 9.9515 · 6,532,328 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6d605b70dcd3148abe8c0250b78fdfbf76a8d6872af59993eef4538dbd6de929

View on Chainz ↗

Height

#271,036

Difficulty

9.951523

Transactions

Size

1.65 KB

Version

Bits

09f39701

Nonce

98,432

Timestamp

11/24/2013, 9:16:44 AM

Confirmations

6,532,328

Mined by

⛏️ P2SHARGFwanmPmtUdYh6axjv1LvNrLZSHg4jNM

Merkle Root

1b4a3318aad05ce639f864655b0bdf2575e0d7b3299dcb6b151cf237ad4bd70e

Transactions (5)

Coinbase85ce01c8c06ab7…6151f28011d138

1 in → 1 out10.1200 XPM109 B

ARGFwanm…ZSHg4jNM

2d5ea2446001c8…4c8336f597a286

1 in → 2 out10.0600 XPM226 B

AHyHEeYQ…XuELsExj AXk6ioeF…pJ6VDgcA

70aa7b41d69697…e51455ee227797

4 in → 2 out44.8200 XPM669 B

ANvrfAMv…X1dW6Pvo AMSj35t4…12GtKPQA

ac8ab379c2a4fd…9d2b8d66c3efa5

1 in → 2 out7.0112 XPM225 B

AGfZWKmc…CYcuGTci AWPn2Xsq…yZeDRYiW

be0cebb4e4ba5b…c488265fbebf6b

2 in → 2 out2.0569 XPM374 B

AKKoMa7P…tofb1RZy AGsd2Zd9…AQWY5Hd6

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.

1.069 × 10⁹³(94-digit number)

10694026529464770919…95372509559825979199

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

1.069 × 10⁹³(94-digit number)

10694026529464770919…95372509559825979199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.069 × 10⁹³(94-digit number)

10694026529464770919…95372509559825979201

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

2.138 × 10⁹³(94-digit number)

21388053058929541838…90745019119651958399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.138 × 10⁹³(94-digit number)

21388053058929541838…90745019119651958401

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

4.277 × 10⁹³(94-digit number)

42776106117859083677…81490038239303916799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.277 × 10⁹³(94-digit number)

42776106117859083677…81490038239303916801

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

8.555 × 10⁹³(94-digit number)

85552212235718167355…62980076478607833599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.555 × 10⁹³(94-digit number)

85552212235718167355…62980076478607833601

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

1.711 × 10⁹⁴(95-digit number)

17110442447143633471…25960152957215667199

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