Block #231,171

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/28/2013, 6:41:49 AM · Difficulty 9.9404 · 6,584,626 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a399fa95359513d28a4a0d6865b803e2c376b3f5fa3036415607d4e1a14032c5

View on Chainz ↗

Height

#231,171

Difficulty

9.940383

Transactions

Size

2.01 KB

Version

Bits

09f0bcf0

Nonce

89,730

Timestamp

10/28/2013, 6:41:49 AM

Confirmations

6,584,626

Mined by

⛏️ RnAbzECnuDBedJY3UxRC7rvMakRUpsvTrds9

Merkle Root

d4b136efbb3da86a6c0eee8da4c90c2692dc291ae7a0156279b87347c9c667bc

Transactions (1)

Coinbased4b136efbb3da8…b87347c9c667bc

1 in → 56 out10.0900 XPM1.92 KB

AbzECnuD…psvTrds9 AVbjNLpc…e1xsNhVz AZeofunA…qsV9L7JD AUmqvzVP…R7Pd9B3z AeZmMFY8…mjAy5Mi4

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.

1.274 × 10⁹⁴(95-digit number)

12744358292811531314…92640579871087334399

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

1.274 × 10⁹⁴(95-digit number)

12744358292811531314…92640579871087334399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.274 × 10⁹⁴(95-digit number)

12744358292811531314…92640579871087334401

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

2.548 × 10⁹⁴(95-digit number)

25488716585623062628…85281159742174668799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.548 × 10⁹⁴(95-digit number)

25488716585623062628…85281159742174668801

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

5.097 × 10⁹⁴(95-digit number)

50977433171246125256…70562319484349337599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.097 × 10⁹⁴(95-digit number)

50977433171246125256…70562319484349337601

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

1.019 × 10⁹⁵(96-digit number)

10195486634249225051…41124638968698675199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.019 × 10⁹⁵(96-digit number)

10195486634249225051…41124638968698675201

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

2.039 × 10⁹⁵(96-digit number)

20390973268498450102…82249277937397350399

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 #231,171

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