Block #270,605

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/24/2013, 1:54:18 AM · Difficulty 9.9516 · 6,539,178 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

85f5cc19457bd395ea381c2ce4e6b70ae13fe54a26bc80d283bea775d588a79d

View on Chainz ↗

Height

#270,605

Difficulty

9.951617

Transactions

Size

1.21 KB

Version

Bits

09f39d34

Nonce

133,534

Timestamp

11/24/2013, 1:54:18 AM

Confirmations

6,539,178

Mined by

⛏️ P2SHATcis4iMr9U9hhBSiXdiMB8VabPqdcn1uL

Merkle Root

5dd422479922e7f23eaff11c35b0f961ada2f785ff190523a2a3c7559f0095e0

Transactions (3)

Coinbased4d77e79dae738…39799178c44dc9

1 in → 1 out10.1000 XPM109 B

ATcis4iM…Pqdcn1uL

76ae858778b832…6a6c0e599dbdb2

1 in → 2 out7.0187 XPM226 B

AYQ4R5CB…Kj7A9idh AcGfgBbB…wXXM6hRs

a3b11ed9b50ba0…f9c3619d5a4df4

5 in → 2 out8.8710 XPM815 B

AX13Suqs…5uhsumtL AQZoKiHA…J6Vp1Z7W

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.

1.443 × 10⁹³(94-digit number)

14433950754251029445…09461427899751451249

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

1.443 × 10⁹³(94-digit number)

14433950754251029445…09461427899751451249

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.443 × 10⁹³(94-digit number)

14433950754251029445…09461427899751451251

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

2.886 × 10⁹³(94-digit number)

28867901508502058891…18922855799502902499

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.886 × 10⁹³(94-digit number)

28867901508502058891…18922855799502902501

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

5.773 × 10⁹³(94-digit number)

57735803017004117783…37845711599005804999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.773 × 10⁹³(94-digit number)

57735803017004117783…37845711599005805001

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

1.154 × 10⁹⁴(95-digit number)

11547160603400823556…75691423198011609999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.154 × 10⁹⁴(95-digit number)

11547160603400823556…75691423198011610001

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

2.309 × 10⁹⁴(95-digit number)

23094321206801647113…51382846396023219999

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 #270,605

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