Block #379,988

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/28/2014, 10:13:51 PM · Difficulty 10.4179 · 6,428,400 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

86bc9533724eb22d9f32a6a0857036560a03df0dfd2c88cd9e8fb5ed41127554

View on Chainz ↗

Height

#379,988

Difficulty

10.417903

Transactions

Size

1.18 KB

Version

Bits

0a6afbaf

Nonce

381,666

Timestamp

1/28/2014, 10:13:51 PM

Confirmations

6,428,400

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

74c466bb19995140ecbbf985597e3a0529b91e9cd59bc74124004a9d6849365b

Transactions (3)

Coinbase9ec9612ea50209…3a548c475c6032

1 in → 1 out9.2300 XPM110 B

AeKNrjNj…1NEq95Ta

5a0eaec4d64941…bbe63747ae72c9

3 in → 2 out16.6136 XPM520 B

AJYmdQBm…F4wmC7gm AZbg77XB…VRrxrTJG

ca8e17435979cc…adad5aba8cba12

3 in → 1 out3.1255 XPM489 B

AWAZzVuf…TTZAfvqD

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.

6.056 × 10⁹⁷(98-digit number)

60569153319819154538…73622147041330261789

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

6.056 × 10⁹⁷(98-digit number)

60569153319819154538…73622147041330261789

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.056 × 10⁹⁷(98-digit number)

60569153319819154538…73622147041330261791

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

1.211 × 10⁹⁸(99-digit number)

12113830663963830907…47244294082660523579

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.211 × 10⁹⁸(99-digit number)

12113830663963830907…47244294082660523581

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

2.422 × 10⁹⁸(99-digit number)

24227661327927661815…94488588165321047159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.422 × 10⁹⁸(99-digit number)

24227661327927661815…94488588165321047161

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

4.845 × 10⁹⁸(99-digit number)

48455322655855323630…88977176330642094319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.845 × 10⁹⁸(99-digit number)

48455322655855323630…88977176330642094321

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

9.691 × 10⁹⁸(99-digit number)

96910645311710647260…77954352661284188639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.691 × 10⁹⁸(99-digit number)

96910645311710647260…77954352661284188641

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 #379,988

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