Block #201,403

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/9/2013, 3:20:48 PM · Difficulty 9.8912 · 6,591,337 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e618bc0c710d3762ad035dcb0fe8a5d0688a686f9bc31c6ab10fc61ef62f5679

View on Chainz ↗

Height

#201,403

Difficulty

9.891214

Transactions

Size

652 B

Version

Bits

09e4269d

Nonce

46,176

Timestamp

10/9/2013, 3:20:48 PM

Confirmations

6,591,337

Merkle Root

b64028ea6df6a584d0acd20caf6bc93ed0f2bf437be84dfd8c615bc9f79f4795

Transactions (3)

Coinbasec44645ba779b08…58bdfa3da53d8a

1 in → 1 out10.2300 XPM109 B

ARAjKC36…b3FTT18r

62fb80bb2043fb…81cd8854234bae

1 in → 2 out10.2100 XPM227 B

AZiZ3BSK…ouABkYiL ATZW3b3n…yL2TgiBy

be621ebf27120d…e1e37c6e9cca40

1 in → 2 out10.8400 XPM226 B

AW9tJGmj…wi5dexzQ ASUJFtQT…Cqr8nBVx

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.

2.461 × 10⁹⁴(95-digit number)

24611099411097525457…10055457626962945279

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

2.461 × 10⁹⁴(95-digit number)

24611099411097525457…10055457626962945279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.461 × 10⁹⁴(95-digit number)

24611099411097525457…10055457626962945281

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

4.922 × 10⁹⁴(95-digit number)

49222198822195050914…20110915253925890559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.922 × 10⁹⁴(95-digit number)

49222198822195050914…20110915253925890561

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

9.844 × 10⁹⁴(95-digit number)

98444397644390101829…40221830507851781119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.844 × 10⁹⁴(95-digit number)

98444397644390101829…40221830507851781121

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

1.968 × 10⁹⁵(96-digit number)

19688879528878020365…80443661015703562239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.968 × 10⁹⁵(96-digit number)

19688879528878020365…80443661015703562241

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

3.937 × 10⁹⁵(96-digit number)

39377759057756040731…60887322031407124479

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