Block #370,067

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/21/2014, 7:50:43 PM · Difficulty 10.4487 · 6,456,233 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c5c43358c9abbca3d23c61863e5ec63b3780d6a7f445715004c0d42be4b23227

View on Chainz ↗

Height

#370,067

Difficulty

10.448711

Transactions

Size

399 B

Version

Bits

0a72dec0

Nonce

12,820

Timestamp

1/21/2014, 7:50:43 PM

Confirmations

6,456,233

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

6babcfd6e4ebcdab8dd34aa9835200ac2f1287f97583a286ae961d7f46ca8494

Transactions (2)

Coinbase979b67d8a0565e…41212daefb7553

1 in → 1 out9.1600 XPM116 B

AbwWkWZt…kawDhufa

d5965feae69a0b…5d1dfc83c45a94

1 in → 1 out1.1338 XPM192 B

ARZVEKfH…S8hZNgTK

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.

2.169 × 10⁹⁷(98-digit number)

21696871382639660350…28658447275065820959

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

2.169 × 10⁹⁷(98-digit number)

21696871382639660350…28658447275065820959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.169 × 10⁹⁷(98-digit number)

21696871382639660350…28658447275065820961

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

4.339 × 10⁹⁷(98-digit number)

43393742765279320700…57316894550131641919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.339 × 10⁹⁷(98-digit number)

43393742765279320700…57316894550131641921

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

8.678 × 10⁹⁷(98-digit number)

86787485530558641400…14633789100263283839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.678 × 10⁹⁷(98-digit number)

86787485530558641400…14633789100263283841

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

1.735 × 10⁹⁸(99-digit number)

17357497106111728280…29267578200526567679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.735 × 10⁹⁸(99-digit number)

17357497106111728280…29267578200526567681

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

3.471 × 10⁹⁸(99-digit number)

34714994212223456560…58535156401053135359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.471 × 10⁹⁸(99-digit number)

34714994212223456560…58535156401053135361

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 #370,067

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