Block #282,938

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/29/2013, 1:42:00 PM · Difficulty 9.9801 · 6,512,504 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0661705c18e5004f1b15f5943463b3dd42698326841093fbc46d891bb31a828e

View on Chainz ↗

Height

#282,938

Difficulty

9.980138

Transactions

Size

967 B

Version

Bits

09faea57

Nonce

76,398

Timestamp

11/29/2013, 1:42:00 PM

Confirmations

6,512,504

Mined by

⛏️ :QaRAWZd1qVJsLEYJ7QkpZDB3cXqFz9pj9yfPa

Merkle Root

97ec1404d7c6a7c45e0ae5c1ccc5885a6796c80eeaa94ab3ce39e4fecddb8faf

Transactions (1)

Coinbase97ec1404d7c6a7…39e4fecddb8faf

1 in → 24 out10.0200 XPM879 B

AWZd1qVJ…9pj9yfPa AainKTwX…96JoTYMU ASpiwtxk…KjGDrh4X AHTTUHKB…g8V7VRLq AHAi4PDp…e5tL4csy

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.

3.577 × 10⁹⁰(91-digit number)

35770951375183047283…70451422431542924799

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

3.577 × 10⁹⁰(91-digit number)

35770951375183047283…70451422431542924799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.577 × 10⁹⁰(91-digit number)

35770951375183047283…70451422431542924801

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

7.154 × 10⁹⁰(91-digit number)

71541902750366094566…40902844863085849599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.154 × 10⁹⁰(91-digit number)

71541902750366094566…40902844863085849601

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

1.430 × 10⁹¹(92-digit number)

14308380550073218913…81805689726171699199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.430 × 10⁹¹(92-digit number)

14308380550073218913…81805689726171699201

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

2.861 × 10⁹¹(92-digit number)

28616761100146437826…63611379452343398399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.861 × 10⁹¹(92-digit number)

28616761100146437826…63611379452343398401

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

5.723 × 10⁹¹(92-digit number)

57233522200292875652…27222758904686796799

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