Block #1,491,305

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/10/2016, 2:18:25 PM · Difficulty 10.6847 · 5,318,650 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a56e95ae4da1bfb9198b206f1a8a905f625caa2437c48c22615704bd2d25df6a

View on Chainz ↗

Height

#1,491,305

Difficulty

10.684709

Transactions

Size

12.02 KB

Version

Bits

0aaf4917

Nonce

494,830,498

Timestamp

3/10/2016, 2:18:25 PM

Confirmations

5,318,650

Mined by

⛏️ P2SHAQ2nTEVxGGwbJKtwNBW4mPoraxtR8Wbxge

Merkle Root

4d243033a602e456190d439d1bee9b20788f050f1fb013d51f645a6c1af9d005

Transactions (3)

Coinbase01d7823675fe2e…fa4c5b9c42bdbe

1 in → 1 out8.8800 XPM109 B

AQ2nTEVx…tR8Wbxge

1721fd07421c7c…513c0926abe1b3

1 in → 1 out7.9900 XPM192 B

AULJqW7T…TL2PLdFs

9827c5c975cc96…1f11ab6cf20653

80 in → 2 out162.7699 XPM11.64 KB

ASZvfDpF…XNPTxycJ AQHE5e6H…xDwU3vYU

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.

3.945 × 10⁹³(94-digit number)

39454182027073224431…46951387591175042559

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

3.945 × 10⁹³(94-digit number)

39454182027073224431…46951387591175042559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.945 × 10⁹³(94-digit number)

39454182027073224431…46951387591175042561

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

7.890 × 10⁹³(94-digit number)

78908364054146448863…93902775182350085119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.890 × 10⁹³(94-digit number)

78908364054146448863…93902775182350085121

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

1.578 × 10⁹⁴(95-digit number)

15781672810829289772…87805550364700170239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.578 × 10⁹⁴(95-digit number)

15781672810829289772…87805550364700170241

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

3.156 × 10⁹⁴(95-digit number)

31563345621658579545…75611100729400340479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.156 × 10⁹⁴(95-digit number)

31563345621658579545…75611100729400340481

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

6.312 × 10⁹⁴(95-digit number)

63126691243317159090…51222201458800680959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.312 × 10⁹⁴(95-digit number)

63126691243317159090…51222201458800680961

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 #1,491,305

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