Block #1,578,099

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/9/2016, 11:03:25 PM · Difficulty 10.6801 · 5,234,881 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

da6b85bf9961dcf15d34862eb2364ad10b412583015aebc23391da358d9ac75f

View on Chainz ↗

Height

#1,578,099

Difficulty

10.680077

Transactions

Size

2.04 KB

Version

Bits

0aae198c

Nonce

1,109,297,382

Timestamp

5/9/2016, 11:03:25 PM

Confirmations

5,234,881

Mined by

⛏️ P2SHAf4d4qYWDB86SNJ7BsmYXzmfwSrmtNz6mL

Merkle Root

b30f30b268855a03d080b172f12f52c33330f55736d94d64aa1a09a1482c8477

Transactions (2)

Coinbasec324fec12d443e…57ea42d04ebb96

1 in → 1 out8.7700 XPM110 B

Af4d4qYW…rmtNz6mL

dd825d2fabbdab…aa3ad2d23bbce4

1 in → 51 out20.9800 XPM1.85 KB

AevhDukV…KuTgproh AUawQYrR…62zTovci AZ3cZHxS…1qdoLqba AXTxG1Ry…bYA4mE3a AGsdmMAX…zXBXhYCb

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.

8.839 × 10⁹²(93-digit number)

88390494352417193367…20299179007365746879

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

8.839 × 10⁹²(93-digit number)

88390494352417193367…20299179007365746879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.839 × 10⁹²(93-digit number)

88390494352417193367…20299179007365746881

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

1.767 × 10⁹³(94-digit number)

17678098870483438673…40598358014731493759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.767 × 10⁹³(94-digit number)

17678098870483438673…40598358014731493761

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

3.535 × 10⁹³(94-digit number)

35356197740966877347…81196716029462987519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.535 × 10⁹³(94-digit number)

35356197740966877347…81196716029462987521

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

7.071 × 10⁹³(94-digit number)

70712395481933754694…62393432058925975039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.071 × 10⁹³(94-digit number)

70712395481933754694…62393432058925975041

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

1.414 × 10⁹⁴(95-digit number)

14142479096386750938…24786864117851950079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.414 × 10⁹⁴(95-digit number)

14142479096386750938…24786864117851950081

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 #1,578,099

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