Block #1,349,382

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/1/2015, 4:20:28 AM · Difficulty 10.8099 · 5,466,905 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

027023d76affececabc074ad2e117ce2456f96e8c3e6e4c9aba780858902599f

View on Chainz ↗

Height

#1,349,382

Difficulty

10.809916

Transactions

Size

1.21 KB

Version

Bits

0acf56aa

Nonce

116,263,550

Timestamp

12/1/2015, 4:20:28 AM

Confirmations

5,466,905

Mined by

⛏️ P2SHAH8whxyL3xDkhwkQsZM6N9vqhfS3L9kiSM

Merkle Root

f425d187df060448c5791226e14a7a77c188af1c4f0ecd492249089003b90de4

Transactions (3)

Coinbase04ceae59215a7d…82ba09d082f677

1 in → 1 out8.5600 XPM109 B

AH8whxyL…S3L9kiSM

42d5e20c1f48ff…000ea3438de1fa

5 in → 2 out10.0243 XPM815 B

AUndj8J3…LDSZH4XY AKKFKgMM…iLppJY7s

dff0d00f55c480…43c61c755e214f

1 in → 2 out6.4071 XPM225 B

AHa2jGeG…GgZFfAq6 AcuM7XiJ…5uND8Jce

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.

1.988 × 10⁹⁵(96-digit number)

19888028186390216715…24566493816377911039

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

1.988 × 10⁹⁵(96-digit number)

19888028186390216715…24566493816377911039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.988 × 10⁹⁵(96-digit number)

19888028186390216715…24566493816377911041

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

3.977 × 10⁹⁵(96-digit number)

39776056372780433431…49132987632755822079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.977 × 10⁹⁵(96-digit number)

39776056372780433431…49132987632755822081

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

7.955 × 10⁹⁵(96-digit number)

79552112745560866863…98265975265511644159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.955 × 10⁹⁵(96-digit number)

79552112745560866863…98265975265511644161

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

1.591 × 10⁹⁶(97-digit number)

15910422549112173372…96531950531023288319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.591 × 10⁹⁶(97-digit number)

15910422549112173372…96531950531023288321

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

3.182 × 10⁹⁶(97-digit number)

31820845098224346745…93063901062046576639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.182 × 10⁹⁶(97-digit number)

31820845098224346745…93063901062046576641

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 #1,349,382

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