Block #1,521,558

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/1/2016, 1:03:52 PM · Difficulty 10.5891 · 5,312,364 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9b2bfbc159ddce5e034a2d3d9672171b8b4658d7e3d0406f20412a2dfbb189d8

View on Chainz ↗

Height

#1,521,558

Difficulty

10.589099

Transactions

Size

1.48 KB

Version

Bits

0a96cf35

Nonce

1,524,758,971

Timestamp

4/1/2016, 1:03:52 PM

Confirmations

5,312,364

Mined by

⛏️ P2SHAZafUawjKfrecBr8aHnuUVvVrextcZba27

Merkle Root

950cc4a179d0c9ce85116960a6ddd830b8e2f1544492a2a2e3719fa09ca83bc9

Transactions (2)

Coinbase4e62c652c81c6e…5d19b2679fbea2

1 in → 1 out8.9200 XPM109 B

AZafUawj…xtcZba27

ac57397f232ac2…c7f7bfa600f31b

1 in → 34 out108.3047 XPM1.28 KB

AN67y95R…6ipgwDrW APV3uJc4…nkBW7EEN ARvfdQDN…ob2aPB2y Aa92S436…Bo6pf1ur AGmCgDzF…7qjtnJE6

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.

9.337 × 10⁹⁶(97-digit number)

93378557519628992751…84515320908203089919

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

9.337 × 10⁹⁶(97-digit number)

93378557519628992751…84515320908203089919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.337 × 10⁹⁶(97-digit number)

93378557519628992751…84515320908203089921

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

1.867 × 10⁹⁷(98-digit number)

18675711503925798550…69030641816406179839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.867 × 10⁹⁷(98-digit number)

18675711503925798550…69030641816406179841

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

3.735 × 10⁹⁷(98-digit number)

37351423007851597100…38061283632812359679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.735 × 10⁹⁷(98-digit number)

37351423007851597100…38061283632812359681

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

7.470 × 10⁹⁷(98-digit number)

74702846015703194201…76122567265624719359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.470 × 10⁹⁷(98-digit number)

74702846015703194201…76122567265624719361

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

1.494 × 10⁹⁸(99-digit number)

14940569203140638840…52245134531249438719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.494 × 10⁹⁸(99-digit number)

14940569203140638840…52245134531249438721

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 #1,521,558

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