Block #96,405

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/4/2013, 4:36:15 AM · Difficulty 9.2672 · 6,748,639 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3de8d35a5ada653bc9b42fa1bb58d552c8c4030b93f55d29e21f7873d22906b4

View on Chainz ↗

Height

#96,405

Difficulty

9.267175

Transactions

Size

1.37 KB

Version

Bits

09446597

Nonce

215,343

Timestamp

8/4/2013, 4:36:15 AM

Confirmations

6,748,639

Mined by

⛏️ P2SHAePH5hhNtd5mYReNtuYVUeW2QnB5ED7Cj3

Merkle Root

075ce73e0ba6cf6b43f3565f6b7146bedbad5fa06eab69bcb512fad7d3c4168e

Transactions (5)

Coinbase1a5d1117986208…adbe60a1d35db6

1 in → 1 out11.6700 XPM109 B

AePH5hhN…B5ED7Cj3

93c3fb31da6425…85a03c884f2923

1 in → 2 out11.7600 XPM227 B

Aci28HgZ…KViDinAP APjdtadt…6Br7LuZK

0aa076d36420b3…1b78ee711cdc87

1 in → 2 out11.7600 XPM227 B

ANj8EYij…gPYWogMe ALpthvGg…D1g5z4CT

5202947e428fa9…18a9a3574428b5

1 in → 2 out5.6922 XPM226 B

AZ2Gkqfn…c2UWMhg9 AT65aPYB…hZp57xEB

9034b5f4659644…142507a33c4418

3 in → 2 out2.0568 XPM524 B

AX8GbnkC…JyiQR9Ld Ab7J3fT2…kpCCUxSM

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.

8.477 × 10¹⁰³(104-digit number)

84770894565624313472…95678962580277176899

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

8.477 × 10¹⁰³(104-digit number)

84770894565624313472…95678962580277176899

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.477 × 10¹⁰³(104-digit number)

84770894565624313472…95678962580277176901

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

1.695 × 10¹⁰⁴(105-digit number)

16954178913124862694…91357925160554353799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.695 × 10¹⁰⁴(105-digit number)

16954178913124862694…91357925160554353801

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

3.390 × 10¹⁰⁴(105-digit number)

33908357826249725388…82715850321108707599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.390 × 10¹⁰⁴(105-digit number)

33908357826249725388…82715850321108707601

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

6.781 × 10¹⁰⁴(105-digit number)

67816715652499450777…65431700642217415199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.781 × 10¹⁰⁴(105-digit number)

67816715652499450777…65431700642217415201

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

1.356 × 10¹⁰⁵(106-digit number)

13563343130499890155…30863401284434830399

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 #96,405

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