Block #1,609,753

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/1/2016, 3:15:45 PM · Difficulty 10.6115 · 5,231,799 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8e98f5f665d254cf4806c911ad055cfdf265bbafb98a6c8accff6c5a72ea5200

View on Chainz ↗

Height

#1,609,753

Difficulty

10.611528

Transactions

Size

1.11 KB

Version

Bits

0a9c8d13

Nonce

2,109,140,119

Timestamp

6/1/2016, 3:15:45 PM

Confirmations

5,231,799

Mined by

⛏️ P2SHAQhNHjFgEtwXykCnQuxUcUJiCY5DwGLBfV

Merkle Root

d5cae77dff284cfdc0da215d752cb7ac773ae7b02e98eb12e1f273a2362729dd

Transactions (2)

Coinbase3cacf5d97f2b33…e4caa9db8c25b8

1 in → 1 out8.8800 XPM109 B

AQhNHjFg…5DwGLBfV

f5ad31f08e759d…089e75618d2412

1 in → 23 out163.7026 XPM940 B

Ac6gigQr…kdefxqcC AKiS3exQ…NXWwP1Mq Ae2kAYdw…7cYg8ff6 AVaSCUen…kMhQZ3Ks AdHgHvt7…9AyLpUFX

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.

1.011 × 10⁹⁴(95-digit number)

10117618118964697035…16351947668664370949

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

1.011 × 10⁹⁴(95-digit number)

10117618118964697035…16351947668664370949

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.011 × 10⁹⁴(95-digit number)

10117618118964697035…16351947668664370951

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

2.023 × 10⁹⁴(95-digit number)

20235236237929394070…32703895337328741899

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.023 × 10⁹⁴(95-digit number)

20235236237929394070…32703895337328741901

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

4.047 × 10⁹⁴(95-digit number)

40470472475858788141…65407790674657483799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.047 × 10⁹⁴(95-digit number)

40470472475858788141…65407790674657483801

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

8.094 × 10⁹⁴(95-digit number)

80940944951717576283…30815581349314967599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.094 × 10⁹⁴(95-digit number)

80940944951717576283…30815581349314967601

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

1.618 × 10⁹⁵(96-digit number)

16188188990343515256…61631162698629935199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.618 × 10⁹⁵(96-digit number)

16188188990343515256…61631162698629935201

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 #1,609,753

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