Block #1,275,340

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/10/2015, 10:08:05 AM · Difficulty 10.8248 · 5,542,605 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e83bbc195547a62ed5fc21ee6c1361e3f3301d7777fa80ecdbd921698be508e3

View on Chainz ↗

Height

#1,275,340

Difficulty

10.824780

Transactions

Size

1.71 KB

Version

Bits

0ad324cc

Nonce

1,536,498,964

Timestamp

10/10/2015, 10:08:05 AM

Confirmations

5,542,605

Mined by

⛏️ P2SHAPqBSxqxptEZK4qsVxX3t6pqUcm4SihFK9

Merkle Root

4c19b4e4c45816c0c19324ae8085f32d08c6c600d76c9d3982bd8246f2348d37

Transactions (3)

Coinbase54f318e2cc1007…274a8fcc363b3b

1 in → 1 out8.5400 XPM110 B

APqBSxqx…m4SihFK9

949d70bbbec6be…ada967d99f80c9

5 in → 2 out27.3019 XPM819 B

AWVZoa2C…113KQq9f AYsHKdQ3…XHNpcair

c13a14b87a0321…8056e3b0c95133

1 in → 17 out14.6712 XPM735 B

ASaBJFXH…RW9p4CDF AH9DpbB5…THjJ12an AXye82rf…8sYSnBud ANT6FYei…mwuM7Nif AbVtLPAH…mUSZtgnn

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.

1.284 × 10⁹⁷(98-digit number)

12847158370237697612…84599172174117375999

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

1.284 × 10⁹⁷(98-digit number)

12847158370237697612…84599172174117375999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.284 × 10⁹⁷(98-digit number)

12847158370237697612…84599172174117376001

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

2.569 × 10⁹⁷(98-digit number)

25694316740475395225…69198344348234751999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.569 × 10⁹⁷(98-digit number)

25694316740475395225…69198344348234752001

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

5.138 × 10⁹⁷(98-digit number)

51388633480950790451…38396688696469503999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.138 × 10⁹⁷(98-digit number)

51388633480950790451…38396688696469504001

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

1.027 × 10⁹⁸(99-digit number)

10277726696190158090…76793377392939007999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.027 × 10⁹⁸(99-digit number)

10277726696190158090…76793377392939008001

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

2.055 × 10⁹⁸(99-digit number)

20555453392380316180…53586754785878015999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.055 × 10⁹⁸(99-digit number)

20555453392380316180…53586754785878016001

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 #1,275,340

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