Block #358,392

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/14/2014, 1:40:15 AM · Difficulty 10.3871 · 6,452,418 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

21657ca3c72d30632a3e598c7ad37e7c1e2617a776ed8536321cd9fd13369ad7

View on Chainz ↗

Height

#358,392

Difficulty

10.387107

Transactions

Size

1.23 KB

Version

Bits

0a631975

Nonce

2,480

Timestamp

1/14/2014, 1:40:15 AM

Confirmations

6,452,418

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

fc0aa0857de05c27e7e96120b69b2b52daf341eb7b1c1261d76763668c314724

Transactions (5)

Coinbase1f063eeb5be780…3a78ea5210411a

1 in → 1 out9.2900 XPM116 B

AbwWkWZt…kawDhufa

5638c6789e204b…1eb789bd2927db

2 in → 2 out2.0175 XPM375 B

AKKAVSLM…idV5zh8h AKC7CpqT…bQH4Dnyy

dbab2a1835acaf…bb046009f76dff

1 in → 2 out5.2415 XPM225 B

ARUNew1n…pmqt6HPN AbSYvRZW…DrpTULpi

0efa1fee95a07f…92a712b22a63db

1 in → 2 out3.2217 XPM225 B

AQEG3SVH…ZBXDxnLX AV25xQKv…EgkZn7Z7

d7eeb0dfd3c3c6…e26e82dc3f24ac

1 in → 2 out1.1336 XPM226 B

AG3wqqt2…gASmMsLj AK5eMZv7…7wDmjJxU

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.

4.538 × 10¹⁰⁴(105-digit number)

45387245635067083078…81101423907889670439

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

4.538 × 10¹⁰⁴(105-digit number)

45387245635067083078…81101423907889670439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.538 × 10¹⁰⁴(105-digit number)

45387245635067083078…81101423907889670441

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

9.077 × 10¹⁰⁴(105-digit number)

90774491270134166156…62202847815779340879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.077 × 10¹⁰⁴(105-digit number)

90774491270134166156…62202847815779340881

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

1.815 × 10¹⁰⁵(106-digit number)

18154898254026833231…24405695631558681759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.815 × 10¹⁰⁵(106-digit number)

18154898254026833231…24405695631558681761

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

3.630 × 10¹⁰⁵(106-digit number)

36309796508053666462…48811391263117363519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.630 × 10¹⁰⁵(106-digit number)

36309796508053666462…48811391263117363521

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

7.261 × 10¹⁰⁵(106-digit number)

72619593016107332925…97622782526234727039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.261 × 10¹⁰⁵(106-digit number)

72619593016107332925…97622782526234727041

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 #358,392

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