Block #300,527

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/8/2013, 3:45:15 PM · Difficulty 9.9923 · 6,512,101 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c7a796bbcf4f23c96c7320b28ee2f2ebd6e0f2ac8bfca5037504a5bb7c2face1

View on Chainz ↗

Height

#300,527

Difficulty

9.992311

Transactions

Size

1.75 KB

Version

Bits

09fe081e

Nonce

239,065

Timestamp

12/8/2013, 3:45:15 PM

Confirmations

6,512,101

Mined by

⛏️ aR&APeshfYVKJ2qg4aRhC5FMjPmxg3PKcKMKH

Merkle Root

75a10665a82cfdf85fc500e89ba5a6d091f2caaf1e8ca2ed2ea3d0cd81e03053

Transactions (4)

Coinbasefd9bc35e78137c…08ea566e26a055

1 in → 30 out9.9800 XPM1.06 KB

APeshfYV…3PKcKMKH AcM3ext6…Hwtj9Qp3 AYcLTeXR…bscgPops Acs9SHrk…QJSB8SFG AKwqFUdz…D4jGNKFN

cf990a24480f80…a50fc46b888786

1 in → 1 out10.0100 XPM159 B

AWemhkmh…j1ozL78u

236c6e084205f4…c200b34e865029

1 in → 2 out2598.8896 XPM226 B

AY8RqZEq…xuKhVysF AN7uPvnZ…rftpfHrp

0106ce8947d304…43088ed1d61259

1 in → 2 out2428.0253 XPM227 B

ALzThr48…pj9gmpGL ALxszBno…nzTw21DJ

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.

1.255 × 10⁹⁹(100-digit number)

12558332560368749210…95414944042519828479

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

1.255 × 10⁹⁹(100-digit number)

12558332560368749210…95414944042519828479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.255 × 10⁹⁹(100-digit number)

12558332560368749210…95414944042519828481

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

2.511 × 10⁹⁹(100-digit number)

25116665120737498420…90829888085039656959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.511 × 10⁹⁹(100-digit number)

25116665120737498420…90829888085039656961

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

5.023 × 10⁹⁹(100-digit number)

50233330241474996841…81659776170079313919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.023 × 10⁹⁹(100-digit number)

50233330241474996841…81659776170079313921

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

1.004 × 10¹⁰⁰(101-digit number)

10046666048294999368…63319552340158627839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.004 × 10¹⁰⁰(101-digit number)

10046666048294999368…63319552340158627841

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

2.009 × 10¹⁰⁰(101-digit number)

20093332096589998736…26639104680317255679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.009 × 10¹⁰⁰(101-digit number)

20093332096589998736…26639104680317255681

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 #300,527

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