Block #351,070

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/9/2014, 11:19:37 AM · Difficulty 10.2924 · 6,459,494 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7c35407e1184d8ef8e656c4a3414c4ca54338bde9106f37ccdb4e842b2cc79f2

View on Chainz ↗

Height

#351,070

Difficulty

10.292367

Transactions

Size

2.15 KB

Version

Bits

0a4ad890

Nonce

5,466

Timestamp

1/9/2014, 11:19:37 AM

Confirmations

6,459,494

Mined by

AJzWx2VDShfKP9pKK3jZqTbn4sj4ZSMit5

Merkle Root

1e3ca3d77279d0544ccb5ddb9a8c6ad3bcd895e507a3969936d73ea951f7ceeb

Transactions (4)

Coinbase0f26533ab45608…7ae74e1dbc9fff

1 in → 25 out9.4300 XPM913 B

AJzWx2VD…j4ZSMit5 AZemWJAo…6jhDtieG AYtDvcGs…VuAcA7m7 ARSeozDw…C9HtARnj AUnkFe8H…fvenjA4X

92018a0727cd61…62298d32b6ead8

5 in → 1 out0.7740 XPM781 B

ATbm5nWr…PN4gBvUF

6e6cd94e03654a…9e3429c2949ad4

1 in → 1 out3.0992 XPM193 B

AaUJFJZS…m3VqAiEj

78096f656f271a…1a22e525e378f4

1 in → 2 out3.1117 XPM227 B

ARMpu4iQ…AVWLiWP2 ALzdmJJd…WN4pQeAv

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.

7.830 × 10⁹⁶(97-digit number)

78307054033196968288…02163597021602609279

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

7.830 × 10⁹⁶(97-digit number)

78307054033196968288…02163597021602609279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.830 × 10⁹⁶(97-digit number)

78307054033196968288…02163597021602609281

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

1.566 × 10⁹⁷(98-digit number)

15661410806639393657…04327194043205218559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.566 × 10⁹⁷(98-digit number)

15661410806639393657…04327194043205218561

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

3.132 × 10⁹⁷(98-digit number)

31322821613278787315…08654388086410437119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.132 × 10⁹⁷(98-digit number)

31322821613278787315…08654388086410437121

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

6.264 × 10⁹⁷(98-digit number)

62645643226557574630…17308776172820874239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.264 × 10⁹⁷(98-digit number)

62645643226557574630…17308776172820874241

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

1.252 × 10⁹⁸(99-digit number)

12529128645311514926…34617552345641748479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.252 × 10⁹⁸(99-digit number)

12529128645311514926…34617552345641748481

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 #351,070

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