Block #273,839

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/26/2013, 12:19:48 AM · Difficulty 9.9558 · 6,522,343 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

21edd0617af2b957e779dc2929f22887f2dfb2eb18e6ca67ec4761f263b6bb8f

View on Chainz ↗

Height

#273,839

Difficulty

9.955847

Transactions

Size

5.21 KB

Version

Bits

09f4b25f

Nonce

113,566

Timestamp

11/26/2013, 12:19:48 AM

Confirmations

6,522,343

Mined by

⛏️ -aRAVzhvfTX6hcvuz5akKkM7Fnv6uZzNJYq61

Merkle Root

6a453d56aed7577a0769708df1dc4fd4eca44e82e9b462213fa6391a9109fc3f

Transactions (4)

Coinbased23f292b4011b9…ed5ee2bb2020df

1 in → 28 out10.0500 XPM1015 B

AVzhvfTX…ZzNJYq61 AWMrD5hP…ZwsoxvZ3 APvpz12N…NjdsxTYA AXNGaZSd…oNaxk7D6 AKH3Kyz4…cbY9pVtN

a1e38ca6cdbc2a…c91a641c6351a4

20 in → 2 out4.0100 XPM2.96 KB

AYp7FrKY…Nepxxvvj Ab2GmNuL…bdQ6PujW

77993d0a9f5735…80108e3e307e41

4 in → 2 out1.0100 XPM668 B

Ab2GmNuL…bdQ6PujW AVLVKJAk…dD83xeFG

0d6928624f50ec…9d52c10ae324a4

3 in → 2 out1.6100 XPM522 B

AM1PPE9a…VMPQaGHt AZJQC1ur…xq7vuVix

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.

5.691 × 10⁹¹(92-digit number)

56915487119655408336…76315995856050077439

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

5.691 × 10⁹¹(92-digit number)

56915487119655408336…76315995856050077439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.691 × 10⁹¹(92-digit number)

56915487119655408336…76315995856050077441

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

1.138 × 10⁹²(93-digit number)

11383097423931081667…52631991712100154879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.138 × 10⁹²(93-digit number)

11383097423931081667…52631991712100154881

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

2.276 × 10⁹²(93-digit number)

22766194847862163334…05263983424200309759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.276 × 10⁹²(93-digit number)

22766194847862163334…05263983424200309761

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

4.553 × 10⁹²(93-digit number)

45532389695724326669…10527966848400619519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.553 × 10⁹²(93-digit number)

45532389695724326669…10527966848400619521

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

9.106 × 10⁹²(93-digit number)

91064779391448653338…21055933696801239039

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