Block #265,903

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/20/2013, 12:15:06 AM · Difficulty 9.9614 · 6,530,000 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

bbc912b051857c4c4d87d7264b84455815d84c4503c2c4f0ab5a439038456d77

View on Chainz ↗

Height

#265,903

Difficulty

9.961371

Transactions

Size

1.84 KB

Version

Bits

09f61c70

Nonce

32,244

Timestamp

11/20/2013, 12:15:06 AM

Confirmations

6,530,000

Mined by

⛏️ aRAVzhvfTX6hcvuz5akKkM7Fnv6uZzNJYq61

Merkle Root

7b7b069bdbe6948271e5af21f57f2cb1a7895c39925ab19cd54c60a1c29b3971

Transactions (1)

Coinbase7b7b069bdbe694…4c60a1c29b3971

1 in → 51 out10.0400 XPM1.75 KB

AVzhvfTX…ZzNJYq61 AFqKfjez…qX9Ace3g APZy8y6E…QZaGQjfp ANHbaxZp…XjnHCJJs AeNjg8HA…9AkdpcSC

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.

2.274 × 10⁹⁴(95-digit number)

22746612406989869439…04341454143901364799

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

2.274 × 10⁹⁴(95-digit number)

22746612406989869439…04341454143901364799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.274 × 10⁹⁴(95-digit number)

22746612406989869439…04341454143901364801

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

4.549 × 10⁹⁴(95-digit number)

45493224813979738878…08682908287802729599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.549 × 10⁹⁴(95-digit number)

45493224813979738878…08682908287802729601

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

9.098 × 10⁹⁴(95-digit number)

90986449627959477756…17365816575605459199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.098 × 10⁹⁴(95-digit number)

90986449627959477756…17365816575605459201

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

1.819 × 10⁹⁵(96-digit number)

18197289925591895551…34731633151210918399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.819 × 10⁹⁵(96-digit number)

18197289925591895551…34731633151210918401

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

3.639 × 10⁹⁵(96-digit number)

36394579851183791102…69463266302421836799

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