Block #324,475

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/22/2013, 9:01:19 AM · Difficulty 10.2054 · 6,493,209 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

43fad6528d78ca78d35c4f465c26e2476149934e4892a10cfc70155ff457b2ce

View on Chainz ↗

Height

#324,475

Difficulty

10.205440

Transactions

Size

902 B

Version

Bits

0a3497b8

Nonce

36,105

Timestamp

12/22/2013, 9:01:19 AM

Confirmations

6,493,209

Mined by

⛏️ {aR`AQ8QAT3JKsV1xD6zC94z9djnpJrCFKuVbR

Merkle Root

afccc294df63c34567b2b6add3ffb326b5d3bafbca537e3c4e1e43cad16a9deb

Transactions (1)

Coinbaseafccc294df63c3…1e43cad16a9deb

1 in → 22 out9.5900 XPM811 B

AQ8QAT3J…rCFKuVbR Ad9pSzHt…cpJ3y2zz Aac9Hjdg…P4ktypc3 AZ2pPuKg…95SN2Yr7 APeshfYV…3PKcKMKH

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.

1.507 × 10⁹⁷(98-digit number)

15072541215183788191…53986552649243066879

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

1.507 × 10⁹⁷(98-digit number)

15072541215183788191…53986552649243066879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.507 × 10⁹⁷(98-digit number)

15072541215183788191…53986552649243066881

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

3.014 × 10⁹⁷(98-digit number)

30145082430367576382…07973105298486133759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.014 × 10⁹⁷(98-digit number)

30145082430367576382…07973105298486133761

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

6.029 × 10⁹⁷(98-digit number)

60290164860735152764…15946210596972267519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.029 × 10⁹⁷(98-digit number)

60290164860735152764…15946210596972267521

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

1.205 × 10⁹⁸(99-digit number)

12058032972147030552…31892421193944535039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.205 × 10⁹⁸(99-digit number)

12058032972147030552…31892421193944535041

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

2.411 × 10⁹⁸(99-digit number)

24116065944294061105…63784842387889070079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.411 × 10⁹⁸(99-digit number)

24116065944294061105…63784842387889070081

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 #324,475

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