Block #1,528,904

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/6/2016, 10:55:12 AM · Difficulty 10.6116 · 5,281,533 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3525fc2f055eb041e5d8c15b30b40f501b39a7176dacb29f57919bebaca5e7e7

View on Chainz ↗

Height

#1,528,904

Difficulty

10.611618

Transactions

Size

2.80 KB

Version

Bits

0a9c92f9

Nonce

794,535,336

Timestamp

4/6/2016, 10:55:12 AM

Confirmations

5,281,533

Mined by

⛏️ P2SHAeQn6S6D1ykozVuHKpd8KytpsM96foPh2v

Merkle Root

5f76ccdc6b3f6c7fa001c51bcf36ff8b70ed9a958931114acea5d918846ad513

Transactions (3)

Coinbase26a681095310e8…b644b334be2605

1 in → 1 out8.9150 XPM109 B

AeQn6S6D…96foPh2v

4ea7b292319400…46f94e79275899

1 in → 2 out0.9953 XPM225 B

ANMnPtEd…bkrxcQ7s AJTPoJai…ayrGbSQ2

b4853bb0bd4e89…a157f4e4d2971c

16 in → 2 out135.0600 XPM2.39 KB

AZfpenV5…rwmGKH6q AG7ViNMB…vXme1US8

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.

4.664 × 10⁹⁵(96-digit number)

46649113433808270462…44746256364402639679

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

4.664 × 10⁹⁵(96-digit number)

46649113433808270462…44746256364402639679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.664 × 10⁹⁵(96-digit number)

46649113433808270462…44746256364402639681

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

9.329 × 10⁹⁵(96-digit number)

93298226867616540925…89492512728805279359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.329 × 10⁹⁵(96-digit number)

93298226867616540925…89492512728805279361

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

1.865 × 10⁹⁶(97-digit number)

18659645373523308185…78985025457610558719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.865 × 10⁹⁶(97-digit number)

18659645373523308185…78985025457610558721

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

3.731 × 10⁹⁶(97-digit number)

37319290747046616370…57970050915221117439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.731 × 10⁹⁶(97-digit number)

37319290747046616370…57970050915221117441

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

7.463 × 10⁹⁶(97-digit number)

74638581494093232740…15940101830442234879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.463 × 10⁹⁶(97-digit number)

74638581494093232740…15940101830442234881

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 #1,528,904

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