Block #453,428

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/21/2014, 7:23:02 AM · Difficulty 10.3866 · 6,354,738 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f235f0f1ec9eb0f6dd3f3e78f97b6c9cb3f5785fd3500db37e35cb04296988be

View on Chainz ↗

Height

#453,428

Difficulty

10.386641

Transactions

Size

6.92 KB

Version

Bits

0a62faea

Nonce

254,744

Timestamp

3/21/2014, 7:23:02 AM

Confirmations

6,354,738

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

31f35d8a2e022b4959edff15643afaa51803bf731090fec55d38d5399106d640

Transactions (3)

Coinbase67d419218c41f3…c9522e45fc3cf3

1 in → 1 out9.3400 XPM110 B

AeKNrjNj…1NEq95Ta

7bc9f61c9eebc4…42df2a76c87048

4 in → 5 out12.2769 XPM737 B

AcacZaAu…7XaX5VD6 AXHFnvkB…yXdZX2Fh AHbu8w6V…13P7BwSQ AKc9Rmjx…Bir3N5mm AeKNrjNj…1NEq95Ta

8be2c63e1a1072…566f0d011f4dbe

41 in → 2 out44.4227 XPM6.00 KB

Aa7NrPBY…Wj2snm9e AV14vbFG…a1ih57x4

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.

9.082 × 10¹⁰⁰(101-digit number)

90820237540189640301…95246711119398748479

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

9.082 × 10¹⁰⁰(101-digit number)

90820237540189640301…95246711119398748479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.082 × 10¹⁰⁰(101-digit number)

90820237540189640301…95246711119398748481

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

1.816 × 10¹⁰¹(102-digit number)

18164047508037928060…90493422238797496959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.816 × 10¹⁰¹(102-digit number)

18164047508037928060…90493422238797496961

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

3.632 × 10¹⁰¹(102-digit number)

36328095016075856120…80986844477594993919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.632 × 10¹⁰¹(102-digit number)

36328095016075856120…80986844477594993921

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

7.265 × 10¹⁰¹(102-digit number)

72656190032151712241…61973688955189987839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.265 × 10¹⁰¹(102-digit number)

72656190032151712241…61973688955189987841

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

1.453 × 10¹⁰²(103-digit number)

14531238006430342448…23947377910379975679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.453 × 10¹⁰²(103-digit number)

14531238006430342448…23947377910379975681

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 #453,428

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