Block #397,021

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/9/2014, 7:10:29 PM · Difficulty 10.4162 · 6,409,288 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ac6a7e04e7bd6c7e6e2924350c94f234bb29a7cdbf604ebfcd3310b5f4df5897

View on Chainz ↗

Height

#397,021

Difficulty

10.416206

Transactions

Size

1.23 KB

Version

Bits

0a6a8c82

Nonce

51,336

Timestamp

2/9/2014, 7:10:29 PM

Confirmations

6,409,288

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

8b98a24a5d103962f1670c1a302df9701bfc30aca39a5373bd28e40b55e77aad

Transactions (5)

Coinbase3d703259a355c0…7525c29dfe5701

1 in → 1 out9.2400 XPM116 B

AbwWkWZt…kawDhufa

8457f2cae1ad0c…a8e54210f2becc

1 in → 2 out6.1321 XPM226 B

AZ42u36J…wJ747vGW AJtKhSB8…jbGJEzbR

147f16da2d281b…4ac6e30b014166

1 in → 2 out2.0381 XPM226 B

AemgbRiM…JgPEKwFg AZCYuzLf…UH9NH8FB

cfcb97c93b41a2…9a511f0c4f5fbd

1 in → 2 out5.1011 XPM227 B

AJY4dKtF…BgEZkZFu AZrcmXs8…aU3yNkk6

bd10286be894c4…728720ee6d4038

2 in → 2 out1.0650 XPM375 B

AN6bAFEn…Pxsc8CgB ATuYheEo…MiATB6Hn

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.

1.936 × 10⁹⁸(99-digit number)

19367443043511471817…58339223948255510399

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

1.936 × 10⁹⁸(99-digit number)

19367443043511471817…58339223948255510399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.936 × 10⁹⁸(99-digit number)

19367443043511471817…58339223948255510401

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

3.873 × 10⁹⁸(99-digit number)

38734886087022943635…16678447896511020799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.873 × 10⁹⁸(99-digit number)

38734886087022943635…16678447896511020801

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

7.746 × 10⁹⁸(99-digit number)

77469772174045887270…33356895793022041599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.746 × 10⁹⁸(99-digit number)

77469772174045887270…33356895793022041601

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

1.549 × 10⁹⁹(100-digit number)

15493954434809177454…66713791586044083199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.549 × 10⁹⁹(100-digit number)

15493954434809177454…66713791586044083201

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

3.098 × 10⁹⁹(100-digit number)

30987908869618354908…33427583172088166399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.098 × 10⁹⁹(100-digit number)

30987908869618354908…33427583172088166401

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 #397,021

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