Block #160,025

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/11/2013, 2:47:55 PM · Difficulty 9.8624 · 6,649,077 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

88c7cfdb75ef2fbe094c445be9c84d9f29e57d821e86d4caf23b83ab897fc63a

View on Chainz ↗

Height

#160,025

Difficulty

9.862360

Transactions

Size

3.69 KB

Version

Bits

09dcc3a1

Nonce

32,567

Timestamp

9/11/2013, 2:47:55 PM

Confirmations

6,649,077

Mined by

⛏️ P2SHAJrqveAUDEwHfFJXB28m76UFuaEGDxonVe

Merkle Root

0ca759f186e9ad82af796f3023f8db10805a8d1b73bd9e0ed145f1bbcbd989a5

Transactions (4)

Coinbase5b14af2f10249a…873fabca2a5296

1 in → 1 out10.3200 XPM109 B

AJrqveAU…EGDxonVe

79657294065f80…eb79dba5d48d6b

19 in → 2 out400.0185 XPM2.63 KB

AcTVDkS8…xDfRv4cg AajUaRLs…nxUAtzch

80f0534a341705…9b54f81d92c944

2 in → 2 out16.1167 XPM374 B

AbENH6Lh…vEsYfVSd AYj4hVoE…FFQUi7GP

fbac422158def4…00b0c57cbf6d8b

3 in → 2 out2.0348 XPM522 B

ANsZYAZy…wSk4mkms ANBJLi5a…iJbxfBmx

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.

4.379 × 10⁹²(93-digit number)

43795642917664485037…81318579126321802959

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

4.379 × 10⁹²(93-digit number)

43795642917664485037…81318579126321802959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.379 × 10⁹²(93-digit number)

43795642917664485037…81318579126321802961

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

8.759 × 10⁹²(93-digit number)

87591285835328970074…62637158252643605919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.759 × 10⁹²(93-digit number)

87591285835328970074…62637158252643605921

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

1.751 × 10⁹³(94-digit number)

17518257167065794014…25274316505287211839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.751 × 10⁹³(94-digit number)

17518257167065794014…25274316505287211841

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

3.503 × 10⁹³(94-digit number)

35036514334131588029…50548633010574423679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.503 × 10⁹³(94-digit number)

35036514334131588029…50548633010574423681

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

7.007 × 10⁹³(94-digit number)

70073028668263176059…01097266021148847359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.007 × 10⁹³(94-digit number)

70073028668263176059…01097266021148847361

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #160,025

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