Block #297,656

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/6/2013, 6:03:03 PM · Difficulty 9.9920 · 6,545,559 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4fa2a3cf6f27c7c0208810d8fdeda5c862303a3631e3f39d4cf842251ad29e02

View on Chainz ↗

Height

#297,656

Difficulty

9.992018

Transactions

Size

1.51 KB

Version

Bits

09fdf4e5

Nonce

90,744

Timestamp

12/6/2013, 6:03:03 PM

Confirmations

6,545,559

Mined by

⛏️ aRAPeshfYVKJ2qg4aRhC5FMjPmxg3PKcKMKH

Merkle Root

07e8a09263c52e3b1ff4d22ed98a48f261a35775bdb088e5839313483747254a

Transactions (4)

Coinbase77082b05870615…1d042bf09861de

1 in → 25 out10.0000 XPM912 B

APeshfYV…3PKcKMKH ARzXge7S…CEjL5oYm AVgWEdEg…dNjtC3xf AQyr8Lw3…hs4nt3Pn Acskt6D1…Db4ci1L8

4159bc8e141c01…7c0a2ccc1d636e

1 in → 1 out10.1000 XPM158 B

AXRhud4t…V3633Waj

7b479d12518b17…6531cef89dbf52

1 in → 1 out10.0000 XPM159 B

AWCHeidF…jKUZAG6U

ea55b9dbf2f102…99bf2eb367b255

1 in → 2 out4.0225 XPM225 B

AFyvS8tA…ja4VHgNh AXXR6Von…cakZEkNh

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.

1.100 × 10¹⁰⁰(101-digit number)

11005567132870208675…40903318627436921579

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

1.100 × 10¹⁰⁰(101-digit number)

11005567132870208675…40903318627436921579

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.100 × 10¹⁰⁰(101-digit number)

11005567132870208675…40903318627436921581

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

2.201 × 10¹⁰⁰(101-digit number)

22011134265740417351…81806637254873843159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.201 × 10¹⁰⁰(101-digit number)

22011134265740417351…81806637254873843161

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

4.402 × 10¹⁰⁰(101-digit number)

44022268531480834702…63613274509747686319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.402 × 10¹⁰⁰(101-digit number)

44022268531480834702…63613274509747686321

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

8.804 × 10¹⁰⁰(101-digit number)

88044537062961669404…27226549019495372639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.804 × 10¹⁰⁰(101-digit number)

88044537062961669404…27226549019495372641

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

1.760 × 10¹⁰¹(102-digit number)

17608907412592333880…54453098038990745279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.760 × 10¹⁰¹(102-digit number)

17608907412592333880…54453098038990745281

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 #297,656

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