Block #381,420

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/29/2014, 11:46:17 PM · Difficulty 10.4062 · 6,435,256 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

cb796d3e94d72143f4c9d3b4d3e48cf783748c8b87b124df8425096fdb04ff38

View on Chainz ↗

Height

#381,420

Difficulty

10.406224

Transactions

Size

1.58 KB

Version

Bits

0a67fe4b

Nonce

5,389

Timestamp

1/29/2014, 11:46:17 PM

Confirmations

6,435,256

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

cf049ec535edb396e76a8b80d69333af9dd4034b478eaf9eaaafedff6d21b4fb

Transactions (4)

Coinbase707f3f35b47f86…ca4ffae0ff935b

1 in → 1 out9.2600 XPM116 B

AbwWkWZt…kawDhufa

f641446519b4a7…c0c9792d39a639

5 in → 10 out28.4128 XPM989 B

AbupveME…uA8GBpWY AFuALAGn…X8UFb5wk Ad1oK5BF…sRvSLRDv AVKfZvtY…sCa4NTcM AeKNrjNj…1NEq95Ta

ed95a83751d5a9…b7e1ab935bb9b1

1 in → 2 out9.0358 XPM226 B

AaGnFpwC…ar9zTZJF AX66oMAZ…MAgwr36y

7cbf6af153dcb9…0d5ca6da0c130c

1 in → 1 out3.0155 XPM192 B

AKJfr8p1…FH3eY8Nc

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.

1.022 × 10⁹⁵(96-digit number)

10225738640341056480…64898602867077340479

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

1.022 × 10⁹⁵(96-digit number)

10225738640341056480…64898602867077340479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.022 × 10⁹⁵(96-digit number)

10225738640341056480…64898602867077340481

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

2.045 × 10⁹⁵(96-digit number)

20451477280682112960…29797205734154680959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.045 × 10⁹⁵(96-digit number)

20451477280682112960…29797205734154680961

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

4.090 × 10⁹⁵(96-digit number)

40902954561364225921…59594411468309361919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.090 × 10⁹⁵(96-digit number)

40902954561364225921…59594411468309361921

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

8.180 × 10⁹⁵(96-digit number)

81805909122728451843…19188822936618723839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.180 × 10⁹⁵(96-digit number)

81805909122728451843…19188822936618723841

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

1.636 × 10⁹⁶(97-digit number)

16361181824545690368…38377645873237447679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.636 × 10⁹⁶(97-digit number)

16361181824545690368…38377645873237447681

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 #381,420

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