Block #182,210

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/27/2013, 3:19:52 AM · Difficulty 9.8591 · 6,626,507 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a33ca1bc58f10b0a01853e174f1fecf6832ce04a54e8e2077cd95ca51775efb7

View on Chainz ↗

Height

#182,210

Difficulty

9.859083

Transactions

Size

652 B

Version

Bits

09dbecd9

Nonce

39,642

Timestamp

9/27/2013, 3:19:52 AM

Confirmations

6,626,507

Mined by

⛏️ P2SHAcKRdgjj4E8fv8J7bb8dnUiRM4ZARbbfWZ

Merkle Root

e0ba837dac1fe10bc79d13ef031c7b609398e6dcfe16413c0433a52342f1874b

Transactions (3)

Coinbase81dfc15fb74039…296359659fb1e6

1 in → 1 out10.2900 XPM109 B

AcKRdgjj…ZARbbfWZ

15eef7fbbd9f34…9b12c6d821c1f2

1 in → 2 out10.2500 XPM227 B

AH3dDrPX…iXBYe8ZV AXJ6UXUk…wNX2Jgqo

7abdf37471efba…628a892059fe24

1 in → 2 out5.2232 XPM226 B

AFuBT9Xk…MEDBBhYN AL64Nohk…3LQgrg6D

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.

4.779 × 10⁹³(94-digit number)

47795675161776920181…57237349444873743359

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

4.779 × 10⁹³(94-digit number)

47795675161776920181…57237349444873743359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.779 × 10⁹³(94-digit number)

47795675161776920181…57237349444873743361

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

9.559 × 10⁹³(94-digit number)

95591350323553840363…14474698889747486719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.559 × 10⁹³(94-digit number)

95591350323553840363…14474698889747486721

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

1.911 × 10⁹⁴(95-digit number)

19118270064710768072…28949397779494973439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.911 × 10⁹⁴(95-digit number)

19118270064710768072…28949397779494973441

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

3.823 × 10⁹⁴(95-digit number)

38236540129421536145…57898795558989946879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.823 × 10⁹⁴(95-digit number)

38236540129421536145…57898795558989946881

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

7.647 × 10⁹⁴(95-digit number)

76473080258843072290…15797591117979893759

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 #182,210

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