Block #1,605,189

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/29/2016, 1:29:52 PM · Difficulty 10.6004 · 5,212,313 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

01372a7e59685b2a8e139a3ffda20b8c5418ec039ab68c0141fba4c4ea11272a

View on Chainz ↗

Height

#1,605,189

Difficulty

10.600450

Transactions

Size

1.57 KB

Version

Bits

0a99b712

Nonce

875,539,585

Timestamp

5/29/2016, 1:29:52 PM

Confirmations

5,212,313

Mined by

⛏️ P2SHAUNMwmnn32bvSbf9Ro8C8HUTcWbwuoonMg

Merkle Root

17e9b9cf5c1786647f48920f8e8334485b1723206efb6fea5a47c9cfeff8e0d1

Transactions (2)

Coinbase811aa710b7895c…73a2c2c0d9042c

1 in → 1 out8.9200 XPM109 B

AUNMwmnn…bwuoonMg

6bcc270bc12344…29f7815ab33048

9 in → 2 out4004.2716 XPM1.37 KB

Aarf22Fs…NfpmdsQA 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.

1.344 × 10⁹⁴(95-digit number)

13440472264306037556…24513338769695380179

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

1.344 × 10⁹⁴(95-digit number)

13440472264306037556…24513338769695380179

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.344 × 10⁹⁴(95-digit number)

13440472264306037556…24513338769695380181

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

2.688 × 10⁹⁴(95-digit number)

26880944528612075112…49026677539390760359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.688 × 10⁹⁴(95-digit number)

26880944528612075112…49026677539390760361

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

5.376 × 10⁹⁴(95-digit number)

53761889057224150225…98053355078781520719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.376 × 10⁹⁴(95-digit number)

53761889057224150225…98053355078781520721

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

1.075 × 10⁹⁵(96-digit number)

10752377811444830045…96106710157563041439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.075 × 10⁹⁵(96-digit number)

10752377811444830045…96106710157563041441

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

2.150 × 10⁹⁵(96-digit number)

21504755622889660090…92213420315126082879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.150 × 10⁹⁵(96-digit number)

21504755622889660090…92213420315126082881

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 #1,605,189

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