Block #188,770

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/1/2013, 9:55:24 AM · Difficulty 9.8711 · 6,613,903 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d8ba8d132df2bd34cee6b293183d049f336e3d5e5ae6947e333f6d8cb62a49d6

View on Chainz ↗

Height

#188,770

Difficulty

9.871143

Transactions

Size

1.27 KB

Version

Bits

09df0340

Nonce

282,683

Timestamp

10/1/2013, 9:55:24 AM

Confirmations

6,613,903

Mined by

⛏️ P2SHAFvfCa1WUvxPh1KkHgJxPR6DVF3pZgbFWa

Merkle Root

aedbb04645348a10315af54013b5b22cd16288f1cd7c8b351b95bc2c9f75df3d

Transactions (3)

Coinbasef38ab685234cbf…9af8d9ccb0bfc1

1 in → 1 out10.2700 XPM110 B

AFvfCa1W…3pZgbFWa

37fffe1f2c5078…34ab9cdcea20ba

2 in → 6 out20.5300 XPM443 B

AKyT5sag…P1gmPYoR ARTJCDz1…oJ6Hi1d9 AcyPVp7N…dDULWcdA ARR7aRH6…ne3DXGXZ ANvtpRa1…QjsraDJz

d833d29b4f0cc1…50c48cb9658395

3 in → 8 out22.4036 XPM657 B

AFq51nP4…FqYfXapg AU5g73DE…hY8WccpK ALd5yTY2…vgfAFVPZ ANvtpRa1…QjsraDJz AGyvi7x2…vr95keMt

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.

6.600 × 10⁹³(94-digit number)

66003117572197796714…85361490962167030399

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

6.600 × 10⁹³(94-digit number)

66003117572197796714…85361490962167030399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.600 × 10⁹³(94-digit number)

66003117572197796714…85361490962167030401

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

1.320 × 10⁹⁴(95-digit number)

13200623514439559342…70722981924334060799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.320 × 10⁹⁴(95-digit number)

13200623514439559342…70722981924334060801

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

2.640 × 10⁹⁴(95-digit number)

26401247028879118685…41445963848668121599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.640 × 10⁹⁴(95-digit number)

26401247028879118685…41445963848668121601

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

5.280 × 10⁹⁴(95-digit number)

52802494057758237371…82891927697336243199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.280 × 10⁹⁴(95-digit number)

52802494057758237371…82891927697336243201

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

1.056 × 10⁹⁵(96-digit number)

10560498811551647474…65783855394672486399

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