Block #324,052

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/22/2013, 1:44:31 AM · Difficulty 10.2078 · 6,493,924 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d75b21069a84dbc76f3df7280aa2a7260f47855bae26f3af11f722560cfc7649

View on Chainz ↗

Height

#324,052

Difficulty

10.207766

Transactions

Size

1006 B

Version

Bits

0a353028

Nonce

236,684

Timestamp

12/22/2013, 1:44:31 AM

Confirmations

6,493,924

Mined by

⛏️ aRCAP5UvYhUvXr8yAGWfLMhV6XKMJvLTDwkdA

Merkle Root

f5e11cc040d9b0900f8dcd93a375101f24acf39cdf17d2e804beb15845f6c171

Transactions (1)

Coinbasef5e11cc040d9b0…beb15845f6c171

1 in → 25 out9.5785 XPM913 B

AP5UvYhU…vLTDwkdA Aac9Hjdg…P4ktypc3 AYtDvcGs…VuAcA7m7 APJPNQaM…8nyTxzkW AYcLTeXR…bscgPops

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.

5.192 × 10¹⁰⁰(101-digit number)

51925188410414829710…10106480877022916799

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

5.192 × 10¹⁰⁰(101-digit number)

51925188410414829710…10106480877022916799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.192 × 10¹⁰⁰(101-digit number)

51925188410414829710…10106480877022916801

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

1.038 × 10¹⁰¹(102-digit number)

10385037682082965942…20212961754045833599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.038 × 10¹⁰¹(102-digit number)

10385037682082965942…20212961754045833601

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

2.077 × 10¹⁰¹(102-digit number)

20770075364165931884…40425923508091667199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.077 × 10¹⁰¹(102-digit number)

20770075364165931884…40425923508091667201

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

4.154 × 10¹⁰¹(102-digit number)

41540150728331863768…80851847016183334399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.154 × 10¹⁰¹(102-digit number)

41540150728331863768…80851847016183334401

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

8.308 × 10¹⁰¹(102-digit number)

83080301456663727536…61703694032366668799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.308 × 10¹⁰¹(102-digit number)

83080301456663727536…61703694032366668801

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 #324,052

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