Block #371,211

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/22/2014, 4:59:09 PM · Difficulty 10.4359 · 6,433,862 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5d6bb67164dbc49c0948e729ded6c21425538ebc2be0a8e95520d790c096425d

View on Chainz ↗

Height

#371,211

Difficulty

10.435886

Transactions

Size

435 B

Version

Bits

0a6f9632

Nonce

18,936

Timestamp

1/22/2014, 4:59:09 PM

Confirmations

6,433,862

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

76de5571cb26dc11cee683b81dca99123cf19054a18335435ad1ef2c0ad6d37a

Transactions (2)

Coinbasea98cc82e3e2bb6…c66dc075dd78bf

1 in → 1 out9.1800 XPM116 B

AbwWkWZt…kawDhufa

a68624bc9a3cf2…2781e2c784c70f

1 in → 2 out1.9813 XPM226 B

AeXZL5oN…siESHime AKcf38Db…pcRRHHkk

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.

3.075 × 10¹⁰¹(102-digit number)

30757185521081528592…73655899583932671999

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

3.075 × 10¹⁰¹(102-digit number)

30757185521081528592…73655899583932671999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.075 × 10¹⁰¹(102-digit number)

30757185521081528592…73655899583932672001

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

6.151 × 10¹⁰¹(102-digit number)

61514371042163057184…47311799167865343999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.151 × 10¹⁰¹(102-digit number)

61514371042163057184…47311799167865344001

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

1.230 × 10¹⁰²(103-digit number)

12302874208432611436…94623598335730687999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.230 × 10¹⁰²(103-digit number)

12302874208432611436…94623598335730688001

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

2.460 × 10¹⁰²(103-digit number)

24605748416865222873…89247196671461375999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.460 × 10¹⁰²(103-digit number)

24605748416865222873…89247196671461376001

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

4.921 × 10¹⁰²(103-digit number)

49211496833730445747…78494393342922751999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.921 × 10¹⁰²(103-digit number)

49211496833730445747…78494393342922752001

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