Block #263,043

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/17/2013, 10:48:17 AM · Difficulty 9.9671 · 6,538,775 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4717a70baa92de2cd1ab869b93b009fb0d3413b81c48451bb6e9842e62c2e75e

View on Chainz ↗

Height

#263,043

Difficulty

9.967137

Transactions

Size

1.88 KB

Version

Bits

09f7964e

Nonce

286,112

Timestamp

11/17/2013, 10:48:17 AM

Confirmations

6,538,775

Mined by

⛏️ aR'=AdxeWJwMdhQmzp8UXQGk2g11qEXPALzofH

Merkle Root

d388f2eeea07a017110c5bbc1371a6ee1ddd8057fdc592a55980107d45c4de83

Transactions (1)

Coinbased388f2eeea07a0…80107d45c4de83

1 in → 52 out10.0300 XPM1.79 KB

AdxeWJwM…XPALzofH AFqKfjez…qX9Ace3g APfbVzNM…GWk2KPXG AQtzUSwq…htAuF3yC AT3ATVPt…Qw6x41k1

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.

1.115 × 10⁹³(94-digit number)

11152293109076355487…55364094718763555839

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

1.115 × 10⁹³(94-digit number)

11152293109076355487…55364094718763555839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.115 × 10⁹³(94-digit number)

11152293109076355487…55364094718763555841

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

2.230 × 10⁹³(94-digit number)

22304586218152710974…10728189437527111679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.230 × 10⁹³(94-digit number)

22304586218152710974…10728189437527111681

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

4.460 × 10⁹³(94-digit number)

44609172436305421949…21456378875054223359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.460 × 10⁹³(94-digit number)

44609172436305421949…21456378875054223361

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

8.921 × 10⁹³(94-digit number)

89218344872610843899…42912757750108446719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.921 × 10⁹³(94-digit number)

89218344872610843899…42912757750108446721

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

1.784 × 10⁹⁴(95-digit number)

17843668974522168779…85825515500216893439

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