Block #161,296

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/12/2013, 2:00:49 PM · Difficulty 9.8590 · 6,633,041 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2be6c759dca8c7f8ea927b7b10324cc11ac652e6cc467f3fae5807718e51ba00

View on Chainz ↗

Height

#161,296

Difficulty

9.859014

Transactions

Size

4.01 KB

Version

Bits

09dbe851

Nonce

40,113

Timestamp

9/12/2013, 2:00:49 PM

Confirmations

6,633,041

Merkle Root

bcaf37b83f1b33c035d21fd3c83696eef7881a4dcc2379e56af4235d981048f1

Transactions (3)

Coinbasefd1562c4d14190…69fe25bd008c92

1 in → 1 out10.3200 XPM109 B

AecT6DSL…gydjUANn

f0c41e09fd542f…a7762c56ca0555

25 in → 1 out255.9114 XPM3.23 KB

AWjfNchA…3r8YxoQa

2771e513288e6a…7cfcb735ea5f10

4 in → 1 out11.0000 XPM604 B

AFz9fXym…wh4UqpkL

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.

3.869 × 10⁹⁰(91-digit number)

38691540951189867225…86600999361753906559

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

3.869 × 10⁹⁰(91-digit number)

38691540951189867225…86600999361753906559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.869 × 10⁹⁰(91-digit number)

38691540951189867225…86600999361753906561

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

7.738 × 10⁹⁰(91-digit number)

77383081902379734451…73201998723507813119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.738 × 10⁹⁰(91-digit number)

77383081902379734451…73201998723507813121

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

1.547 × 10⁹¹(92-digit number)

15476616380475946890…46403997447015626239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.547 × 10⁹¹(92-digit number)

15476616380475946890…46403997447015626241

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

3.095 × 10⁹¹(92-digit number)

30953232760951893780…92807994894031252479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.095 × 10⁹¹(92-digit number)

30953232760951893780…92807994894031252481

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

6.190 × 10⁹¹(92-digit number)

61906465521903787561…85615989788062504959

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