Block #273,268

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/25/2013, 5:20:01 PM · Difficulty 9.9545 · 6,540,814 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4147284a55fc53d0945034add1464a1254aede2428af343825622353f24fa78c

View on Chainz ↗

Height

#273,268

Difficulty

9.954473

Transactions

Size

490 B

Version

Bits

09f45850

Nonce

27,011

Timestamp

11/25/2013, 5:20:01 PM

Confirmations

6,540,814

Mined by

⛏️ t+aRAZ2pPuKgN7GXPJPBLxtm9bkWcE95SN2Yr7

Merkle Root

12c7073db3c88d95be64e73b64fce47fd2169a10361833b8ed328e3f3b17aab6

Transactions (1)

Coinbase12c7073db3c88d…328e3f3b17aab6

1 in → 10 out10.0800 XPM403 B

AZ2pPuKg…95SN2Yr7 AQG9JFWj…UA3LY7Me AUsdND2U…PxHWEPmG AcdRgHjc…2wUWy2B1 AJzWx2VD…j4ZSMit5

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.

3.835 × 10⁸⁸(89-digit number)

38350541714551342859…30147271019550335149

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

3.835 × 10⁸⁸(89-digit number)

38350541714551342859…30147271019550335149

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.835 × 10⁸⁸(89-digit number)

38350541714551342859…30147271019550335151

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

7.670 × 10⁸⁸(89-digit number)

76701083429102685718…60294542039100670299

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.670 × 10⁸⁸(89-digit number)

76701083429102685718…60294542039100670301

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

1.534 × 10⁸⁹(90-digit number)

15340216685820537143…20589084078201340599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.534 × 10⁸⁹(90-digit number)

15340216685820537143…20589084078201340601

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

3.068 × 10⁸⁹(90-digit number)

30680433371641074287…41178168156402681199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.068 × 10⁸⁹(90-digit number)

30680433371641074287…41178168156402681201

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

6.136 × 10⁸⁹(90-digit number)

61360866743282148575…82356336312805362399

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 #273,268

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