Block #161,226

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/12/2013, 12:49:16 PM · Difficulty 9.8591 · 6,645,683 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7cd001405ceb4be26d7882cb0349d08a678971733163f5eca56a8f21bd1a83ea

View on Chainz ↗

Height

#161,226

Difficulty

9.859103

Transactions

Size

2.13 KB

Version

Bits

09dbee2e

Nonce

324,128

Timestamp

9/12/2013, 12:49:16 PM

Confirmations

6,645,683

Mined by

⛏️ P2SHANzqh5ofHkmLaGT2SgpVETduSmLDrBfDTS

Merkle Root

057427db2b78251eab1f94451da7ee4ed6bd99539eaddcfc3d1e673066800885

Transactions (2)

Coinbaseb6e86c489ac57d…81818700d9b400

1 in → 1 out10.3000 XPM109 B

ANzqh5of…LDrBfDTS

daf039b95b0148…269371ef5cde96

17 in → 1 out174.3306 XPM1.94 KB

AbxSykSg…BX71twYi

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.

1.382 × 10⁹³(94-digit number)

13823167447431931615…46020052240994015359

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

1.382 × 10⁹³(94-digit number)

13823167447431931615…46020052240994015359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.382 × 10⁹³(94-digit number)

13823167447431931615…46020052240994015361

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

2.764 × 10⁹³(94-digit number)

27646334894863863230…92040104481988030719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.764 × 10⁹³(94-digit number)

27646334894863863230…92040104481988030721

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

5.529 × 10⁹³(94-digit number)

55292669789727726461…84080208963976061439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.529 × 10⁹³(94-digit number)

55292669789727726461…84080208963976061441

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

1.105 × 10⁹⁴(95-digit number)

11058533957945545292…68160417927952122879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.105 × 10⁹⁴(95-digit number)

11058533957945545292…68160417927952122881

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

2.211 × 10⁹⁴(95-digit number)

22117067915891090584…36320835855904245759

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 #161,226

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