Block #263,266

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/17/2013, 3:45:07 PM · Difficulty 9.9667 · 6,550,946 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8fe131716dae97ffd82fe8057a7f1feffd7b32c7b43509703d789fe033a038cb

View on Chainz ↗

Height

#263,266

Difficulty

9.966658

Transactions

Size

1.43 KB

Version

Bits

09f776e5

Nonce

99,956

Timestamp

11/17/2013, 3:45:07 PM

Confirmations

6,550,946

Mined by

⛏️ P2SHAdGRRh1eP4JFvQMqy7y2pLsryDQmctLb24

Merkle Root

0c68ca1baa685dd17e42b28915bf4bc1b14b2bb4dc44b396b4e700e291746d63

Transactions (4)

Coinbasef70678910a142f…5408d87091450a

1 in → 2 out10.0800 XPM141 B

AdGRRh1e…QmctLb24 AHsw4d6U…EnM8UXNZ

aea8298918ff78…c814e4e5794043

1 in → 2 out0.1400 XPM226 B

AZZpshdo…AFSZwZUx ARbm6c7z…LuqNETUX

21ac3e247c8613…ae4ab76f64e769

1 in → 1 out184.9913 XPM192 B

AQVK2V6U…eKbPEfcz

d1141bd2d4a2c9…56798c999b63ee

5 in → 2 out129.1289 XPM819 B

AdaVKKGe…ugHYQjuU AZdmkNt9…Dk8ffFeU

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.

6.861 × 10⁹⁵(96-digit number)

68619067879548641762…83610677907859473439

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

6.861 × 10⁹⁵(96-digit number)

68619067879548641762…83610677907859473439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.861 × 10⁹⁵(96-digit number)

68619067879548641762…83610677907859473441

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

1.372 × 10⁹⁶(97-digit number)

13723813575909728352…67221355815718946879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.372 × 10⁹⁶(97-digit number)

13723813575909728352…67221355815718946881

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

2.744 × 10⁹⁶(97-digit number)

27447627151819456704…34442711631437893759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.744 × 10⁹⁶(97-digit number)

27447627151819456704…34442711631437893761

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

5.489 × 10⁹⁶(97-digit number)

54895254303638913409…68885423262875787519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.489 × 10⁹⁶(97-digit number)

54895254303638913409…68885423262875787521

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

1.097 × 10⁹⁷(98-digit number)

10979050860727782681…37770846525751575039

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 #263,266

Cookie Preferences