Block #280,143

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/28/2013, 2:17:19 PM · Difficulty 9.9737 · 6,537,041 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1f23cefb9d0150793105afe5a6a7353a0c034cee09c379fbb2db4d68020df7aa

View on Chainz ↗

Height

#280,143

Difficulty

9.973729

Transactions

Size

11.63 KB

Version

Bits

09f9464b

Nonce

36,059

Timestamp

11/28/2013, 2:17:19 PM

Confirmations

6,537,041

Mined by

⛏️ OFaRPy'AWXYBWKPhGt4UM6JfKUZgx3SbUqQAoisBJ

Merkle Root

78238e94357cd4734c9d4112fdade7a6c1d3a6785996009038720fe196fcb672

Transactions (2)

Coinbasef71aa5fbe5104d…d057d753ffec36

1 in → 30 out10.0200 XPM1.06 KB

AWXYBWKP…qQAoisBJ AZ2pPuKg…95SN2Yr7 AbtgNzNb…9Atvu81w AX6xJioT…NymntK8m Ae58nAEb…GFUA15fv

4f2486e8aafd7e…07ccd62878c4c1

72 in → 2 out68.0619 XPM10.48 KB

APRhQN6u…fb8UhP4J AKNvysgH…6JuA8mgm

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.

9.395 × 10¹⁰⁰(101-digit number)

93955902297338389523…97843217625641943039

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

9.395 × 10¹⁰⁰(101-digit number)

93955902297338389523…97843217625641943039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.395 × 10¹⁰⁰(101-digit number)

93955902297338389523…97843217625641943041

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

1.879 × 10¹⁰¹(102-digit number)

18791180459467677904…95686435251283886079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.879 × 10¹⁰¹(102-digit number)

18791180459467677904…95686435251283886081

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

3.758 × 10¹⁰¹(102-digit number)

37582360918935355809…91372870502567772159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.758 × 10¹⁰¹(102-digit number)

37582360918935355809…91372870502567772161

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

7.516 × 10¹⁰¹(102-digit number)

75164721837870711618…82745741005135544319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.516 × 10¹⁰¹(102-digit number)

75164721837870711618…82745741005135544321

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

1.503 × 10¹⁰²(103-digit number)

15032944367574142323…65491482010271088639

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 #280,143

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