Block #262,772

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/17/2013, 4:29:22 AM · Difficulty 9.9678 · 6,564,464 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b545b4ba13c59227d46289ca351697d77a1c6b308e63ade4a4acfe09c64740c8

View on Chainz ↗

Height

#262,772

Difficulty

9.967840

Transactions

Size

541 B

Version

Bits

09f7c45f

Nonce

14,826

Timestamp

11/17/2013, 4:29:22 AM

Confirmations

6,564,464

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

febf1257a482da8142f0aca159f5b5050b11709fa71faaed47f470c5098f1a97

Transactions (2)

Coinbasee21b3fe5152bb8…db0eaa357fe86e

1 in → 1 out10.0600 XPM109 B

AeKNrjNj…1NEq95Ta

0bd394dad4c6fd…64604fe9731425

2 in → 1 out596.6800 XPM340 B

AMSC7hJX…qMSkHHU9

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.

1.727 × 10¹⁰⁰(101-digit number)

17275769011140286170…27488844833327433819

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

1.727 × 10¹⁰⁰(101-digit number)

17275769011140286170…27488844833327433819

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.727 × 10¹⁰⁰(101-digit number)

17275769011140286170…27488844833327433821

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

3.455 × 10¹⁰⁰(101-digit number)

34551538022280572340…54977689666654867639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.455 × 10¹⁰⁰(101-digit number)

34551538022280572340…54977689666654867641

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

6.910 × 10¹⁰⁰(101-digit number)

69103076044561144681…09955379333309735279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.910 × 10¹⁰⁰(101-digit number)

69103076044561144681…09955379333309735281

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

1.382 × 10¹⁰¹(102-digit number)

13820615208912228936…19910758666619470559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.382 × 10¹⁰¹(102-digit number)

13820615208912228936…19910758666619470561

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

2.764 × 10¹⁰¹(102-digit number)

27641230417824457872…39821517333238941119

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 #262,772

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