Block #1,294,482

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/22/2015, 8:49:57 PM · Difficulty 10.8630 · 5,514,781 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

13396c067c229ea07746db5662d7327caa17140e6b0e265b01485cb43ce49163

View on Chainz ↗

Height

#1,294,482

Difficulty

10.862963

Transactions

Size

1.08 KB

Version

Bits

0adceb1e

Nonce

2,006,963,852

Timestamp

10/22/2015, 8:49:57 PM

Confirmations

5,514,781

Mined by

⛏️ P2SHAKF7AV5KbUJFi5bQ7fzRQqkGg3ookVrShz

Merkle Root

1e57768827de20e9ebb3aa3378511574d179dc460da414624061f7bbfc5ff387

Transactions (5)

Coinbase48ae30556ddd30…103d56b862e462

1 in → 1 out8.5000 XPM110 B

AKF7AV5K…ookVrShz

6952c8267690de…0266272e53a6b2

1 in → 2 out7.9651 XPM225 B

APdV1aFA…9Rd7AhZj AGEed55R…9o5EJWws

7a607f75754a66…4a5b626400c7fe

1 in → 2 out7.4173 XPM227 B

AMHwFQ7F…S6fNESwY AeJZ3JqX…xn4ZML6d

59e8380650d3ab…9d664b095ec17b

1 in → 2 out7.3840 XPM227 B

AeBXt8Kg…Lij4qy6D AZp84AN3…xwi9EEnC

9c820c2498cb13…acd70a40a72ea3

1 in → 2 out2.1208 XPM226 B

AU4f4km9…u8UnNcJ8 AXvAkHTU…UbFjuggb

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.

1.684 × 10⁹⁶(97-digit number)

16848814854726239022…17919334343396567039

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

1.684 × 10⁹⁶(97-digit number)

16848814854726239022…17919334343396567039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.684 × 10⁹⁶(97-digit number)

16848814854726239022…17919334343396567041

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

3.369 × 10⁹⁶(97-digit number)

33697629709452478045…35838668686793134079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.369 × 10⁹⁶(97-digit number)

33697629709452478045…35838668686793134081

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

6.739 × 10⁹⁶(97-digit number)

67395259418904956090…71677337373586268159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.739 × 10⁹⁶(97-digit number)

67395259418904956090…71677337373586268161

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

1.347 × 10⁹⁷(98-digit number)

13479051883780991218…43354674747172536319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.347 × 10⁹⁷(98-digit number)

13479051883780991218…43354674747172536321

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

2.695 × 10⁹⁷(98-digit number)

26958103767561982436…86709349494345072639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.695 × 10⁹⁷(98-digit number)

26958103767561982436…86709349494345072641

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 #1,294,482

Cookie Preferences