Block #264,959

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/19/2013, 3:43:59 AM · Difficulty 9.9635 · 6,543,424 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9be551ecae6333c73bf0f4b806655f9677832ba36ffa37a6c378e18490d08485

View on Chainz ↗

Height

#264,959

Difficulty

9.963487

Transactions

Size

35.61 KB

Version

Bits

09f6a716

Nonce

31,895

Timestamp

11/19/2013, 3:43:59 AM

Confirmations

6,543,424

Mined by

⛏️ 11446AdGRRh1eP4JFvQMqy7y2pLsryDQmctLb24

Merkle Root

53b61d06dc52254b01538461ffc4fdf9f9fa2f1c83aa0021f0eb1faad71b5698

Transactions (3)

Coinbasef23c7be1322765…9625a9a188c7a1

1 in → 2 out10.6700 XPM141 B

AdGRRh1e…QmctLb24 Abiw8n3q…ZnZfgvQW

fc8d167774c1db…32852a57e17eb8

236 in → 1 out2000.0000 XPM34.15 KB

AVsbsqKv…t4SX4xb1

db6d76cd84c44a…0445bfdac19666

8 in → 2 out100.0100 XPM1.23 KB

ANhL8wwo…NMkxhntD AHXvGoPJ…ALaqpVuz

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.

1.416 × 10⁹³(94-digit number)

14169249104760317647…86730184193141371689

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

1.416 × 10⁹³(94-digit number)

14169249104760317647…86730184193141371689

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.416 × 10⁹³(94-digit number)

14169249104760317647…86730184193141371691

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

2.833 × 10⁹³(94-digit number)

28338498209520635295…73460368386282743379

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.833 × 10⁹³(94-digit number)

28338498209520635295…73460368386282743381

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

5.667 × 10⁹³(94-digit number)

56676996419041270590…46920736772565486759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.667 × 10⁹³(94-digit number)

56676996419041270590…46920736772565486761

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

1.133 × 10⁹⁴(95-digit number)

11335399283808254118…93841473545130973519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.133 × 10⁹⁴(95-digit number)

11335399283808254118…93841473545130973521

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

2.267 × 10⁹⁴(95-digit number)

22670798567616508236…87682947090261947039

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 #264,959

Cookie Preferences