Block #428,537

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/4/2014, 4:04:33 AM · Difficulty 10.3453 · 6,415,257 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

15521f6d0b954dd30e11537568d53231f0728f804878f24b8b260e24ff73ef2a

View on Chainz ↗

Height

#428,537

Difficulty

10.345304

Transactions

Size

1003 B

Version

Bits

0a5865db

Nonce

3,690

Timestamp

3/4/2014, 4:04:33 AM

Confirmations

6,415,257

Mined by

⛏️ aSPnAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

ed22f27ebd2298262b6ea42d75db78200558f58169d1dcbbdb40342d799de3c3

Transactions (1)

Coinbaseed22f27ebd2298…40342d799de3c3

1 in → 25 out9.3300 XPM913 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AScAzqGc…BZ6tV1vJ AGKhfQo2…h7fBXLX6 ALqxX1WA…hsKjbnXn

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.

5.205 × 10⁹⁵(96-digit number)

52053313125045039932…23563862480355090079

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

5.205 × 10⁹⁵(96-digit number)

52053313125045039932…23563862480355090079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.205 × 10⁹⁵(96-digit number)

52053313125045039932…23563862480355090081

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

1.041 × 10⁹⁶(97-digit number)

10410662625009007986…47127724960710180159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.041 × 10⁹⁶(97-digit number)

10410662625009007986…47127724960710180161

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

2.082 × 10⁹⁶(97-digit number)

20821325250018015972…94255449921420360319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.082 × 10⁹⁶(97-digit number)

20821325250018015972…94255449921420360321

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

4.164 × 10⁹⁶(97-digit number)

41642650500036031945…88510899842840720639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.164 × 10⁹⁶(97-digit number)

41642650500036031945…88510899842840720641

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

8.328 × 10⁹⁶(97-digit number)

83285301000072063891…77021799685681441279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.328 × 10⁹⁶(97-digit number)

83285301000072063891…77021799685681441281

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 #428,537

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