Block #1,566,089

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/30/2016, 4:05:31 PM · Difficulty 10.7557 · 5,251,757 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5cd8490b335d6ff0508ef71714535b6df17080e74c0659a9d87cff25ac98d078

View on Chainz ↗

Height

#1,566,089

Difficulty

10.755651

Transactions

Size

1.28 KB

Version

Bits

0ac17253

Nonce

1,836,778,736

Timestamp

4/30/2016, 4:05:31 PM

Confirmations

5,251,757

Mined by

⛏️ P2SHATMy5frg3Rm7hYjkfT3yYrczxbbfsKmqNS

Merkle Root

90900b07d0c706526d9f637d6de5ce64960d7e32f0fb1781302065425c60a7f4

Transactions (2)

Coinbasef0f7514bef45f5…ef758ad7f35c07

1 in → 1 out8.6500 XPM110 B

ATMy5frg…bfsKmqNS

0625d84df5eeca…8abe209e4c545a

1 in → 28 out201.6317 XPM1.08 KB

AVuGAa8H…c2xBww6K AZJK2yXa…ci7vXBzh AWz1KjjL…8TzR4rmg AQDRamJM…WDFTQomU AYHE76pQ…KaiLyuM4

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.

1.618 × 10⁹⁶(97-digit number)

16187234365870015000…55160233324000563199

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

1.618 × 10⁹⁶(97-digit number)

16187234365870015000…55160233324000563199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.618 × 10⁹⁶(97-digit number)

16187234365870015000…55160233324000563201

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

3.237 × 10⁹⁶(97-digit number)

32374468731740030000…10320466648001126399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.237 × 10⁹⁶(97-digit number)

32374468731740030000…10320466648001126401

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

6.474 × 10⁹⁶(97-digit number)

64748937463480060000…20640933296002252799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.474 × 10⁹⁶(97-digit number)

64748937463480060000…20640933296002252801

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

1.294 × 10⁹⁷(98-digit number)

12949787492696012000…41281866592004505599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.294 × 10⁹⁷(98-digit number)

12949787492696012000…41281866592004505601

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

2.589 × 10⁹⁷(98-digit number)

25899574985392024000…82563733184009011199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.589 × 10⁹⁷(98-digit number)

25899574985392024000…82563733184009011201

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 #1,566,089

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