Block #216,147

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/18/2013, 1:55:17 PM · Difficulty 9.9257 · 6,592,759 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

73f26593b072171431e778bdeec32ec4e9b4b3bdda20769379af3a8702197ff5

View on Chainz ↗

Height

#216,147

Difficulty

9.925684

Transactions

Size

4.51 KB

Version

Bits

09ecf9a0

Nonce

200,369

Timestamp

10/18/2013, 1:55:17 PM

Confirmations

6,592,759

Mined by

⛏️ P2SHAP9VqvUxMvAj94Ggu5qbyD8wnfAkA4rR3E

Merkle Root

7d3aa8e66ca127afe66c2916f3ff6f6aa86c41d7cff780a309d3cd34a8f3f508

Transactions (4)

Coinbase1d943e1718db7a…e13b958441eac4

1 in → 1 out10.2000 XPM109 B

AP9VqvUx…AkA4rR3E

995cf9730abb02…e41c39a6e55d17

11 in → 2 out19.6784 XPM1.67 KB

AcVbkqB1…c531sXdR AR4gFFu7…KqH5akfp

7531a6ff061cd1…e7bc1131244578

2 in → 1 out20.3600 XPM272 B

AY5fgH84…FgYdDHLv

d70f91bd457ff4…ae7e30c982f3a5

16 in → 2 out1.0100 XPM2.39 KB

AetSraPr…fpeH9Z6f AZK2hyLi…LHnLRK5t

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.

2.010 × 10⁹⁴(95-digit number)

20102356176979702830…23480358728021243839

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

2.010 × 10⁹⁴(95-digit number)

20102356176979702830…23480358728021243839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.010 × 10⁹⁴(95-digit number)

20102356176979702830…23480358728021243841

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

4.020 × 10⁹⁴(95-digit number)

40204712353959405661…46960717456042487679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.020 × 10⁹⁴(95-digit number)

40204712353959405661…46960717456042487681

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

8.040 × 10⁹⁴(95-digit number)

80409424707918811323…93921434912084975359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.040 × 10⁹⁴(95-digit number)

80409424707918811323…93921434912084975361

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

1.608 × 10⁹⁵(96-digit number)

16081884941583762264…87842869824169950719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.608 × 10⁹⁵(96-digit number)

16081884941583762264…87842869824169950721

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

3.216 × 10⁹⁵(96-digit number)

32163769883167524529…75685739648339901439

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 #216,147

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