Block #351,578

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/9/2014, 6:56:44 PM · Difficulty 10.2977 · 6,457,223 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

046f12f95df5b84ea5ffe0c8c3cdd5427c963e315afa66c7ec9a4a6d6979f737

View on Chainz ↗

Height

#351,578

Difficulty

10.297724

Transactions

Size

866 B

Version

Bits

0a4c37a7

Nonce

45,645

Timestamp

1/9/2014, 6:56:44 PM

Confirmations

6,457,223

Mined by

⛏️ ZAbopjr7ZNGrUjb1L7deX9XNozHzLTB81mz

Merkle Root

d8b0f83c17ef12bd0093cd00140722a8da248582c70a5ce783b2ba36ca73709d

Transactions (4)

Coinbasede70deb78d5a9c…b01d0e54970d75

1 in → 1 out9.4200 XPM97 B

Abopjr7Z…zLTB81mz

17ce416248463d…5266506bf89038

1 in → 2 out6.0994 XPM226 B

ALhpCfAs…V6tYDMDg ARpzqnUm…DmQAk68w

ccfd350726f2e5…6637b4624d5459

1 in → 2 out2.6011 XPM226 B

AYdsibqM…mpmrx6xz AZDUmrFV…nPRRhaM7

d088ef28f3c8a0…082b748f4bc498

1 in → 2 out3.4140 XPM226 B

AG6PGTdq…VHzYSyK9 AQFvKd6T…NpdyMHFU

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.

2.519 × 10⁹⁶(97-digit number)

25192921133023188628…82986685746382732799

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

2.519 × 10⁹⁶(97-digit number)

25192921133023188628…82986685746382732799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.519 × 10⁹⁶(97-digit number)

25192921133023188628…82986685746382732801

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

5.038 × 10⁹⁶(97-digit number)

50385842266046377257…65973371492765465599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.038 × 10⁹⁶(97-digit number)

50385842266046377257…65973371492765465601

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

1.007 × 10⁹⁷(98-digit number)

10077168453209275451…31946742985530931199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.007 × 10⁹⁷(98-digit number)

10077168453209275451…31946742985530931201

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

2.015 × 10⁹⁷(98-digit number)

20154336906418550902…63893485971061862399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.015 × 10⁹⁷(98-digit number)

20154336906418550902…63893485971061862401

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

4.030 × 10⁹⁷(98-digit number)

40308673812837101805…27786971942123724799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.030 × 10⁹⁷(98-digit number)

40308673812837101805…27786971942123724801

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 #351,578

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