Block #193,589

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/4/2013, 2:49:47 PM · Difficulty 9.8769 · 6,615,372 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b54855b0e8a658e6938c10f7931f2a9c2fe5e051d93a838369b652d1bfec4161

View on Chainz ↗

Height

#193,589

Difficulty

9.876864

Transactions

Size

4.77 KB

Version

Bits

09e07a2a

Nonce

1,164,783,032

Timestamp

10/4/2013, 2:49:47 PM

Confirmations

6,615,372

Mined by

⛏️ 5RNyAeWxj9KgDNTcMKRVBagXZqhphR68s5ydDz

Merkle Root

b260cb596724549bdf6066e3d9f3be26c7159d704e34865c3bb971eb559a7317

Transactions (2)

Coinbase64131d046be96f…24225b1b031d84

1 in → 115 out10.2100 XPM3.88 KB

AeWxj9Kg…68s5ydDz AJFEjLou…q1DYRRGz AVeHc9d8…MRstqd4p ALk3c6sY…okih5vHt AYKPpLgC…TxzhTdBb

ade6dcdff454a9…ca74233bb1d5a2

5 in → 2 out525.0003 XPM819 B

AZH2CfPH…ucCUkaJS AJADixXS…fSVYyLWJ

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.

2.789 × 10⁹⁵(96-digit number)

27898380716725641658…30643399637250790399

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

2.789 × 10⁹⁵(96-digit number)

27898380716725641658…30643399637250790399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.789 × 10⁹⁵(96-digit number)

27898380716725641658…30643399637250790401

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

5.579 × 10⁹⁵(96-digit number)

55796761433451283317…61286799274501580799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.579 × 10⁹⁵(96-digit number)

55796761433451283317…61286799274501580801

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

1.115 × 10⁹⁶(97-digit number)

11159352286690256663…22573598549003161599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.115 × 10⁹⁶(97-digit number)

11159352286690256663…22573598549003161601

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

2.231 × 10⁹⁶(97-digit number)

22318704573380513327…45147197098006323199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.231 × 10⁹⁶(97-digit number)

22318704573380513327…45147197098006323201

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

4.463 × 10⁹⁶(97-digit number)

44637409146761026654…90294394196012646399

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 #193,589

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