Block #193,986

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/4/2013, 8:40:19 PM · Difficulty 9.8781 · 6,633,169 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d42e2fad29e169d5285d1a2379f6dac348df6171af20fa7555831a5204ea37ed

View on Chainz ↗

Height

#193,986

Difficulty

9.878076

Transactions

Size

572 B

Version

Bits

09e0c993

Nonce

21,550

Timestamp

10/4/2013, 8:40:19 PM

Confirmations

6,633,169

Mined by

⛏️ P2SHAbJUC2oSrZY84nuu7WUoHPgJjAcpKam6LK

Merkle Root

816b119921531184599c4272662d7c6d69ddc57fe74fb51db732c6b0fb959136

Transactions (2)

Coinbase0adc991d097fd0…0855a93f84885c

1 in → 1 out10.2400 XPM109 B

AbJUC2oS…cpKam6LK

dcf355f9401b1e…6a762b11f59d9c

2 in → 2 out20.4700 XPM374 B

AbQVuXmJ…qZjmTccE AL1KvDf1…1Jfjqe1k

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.

2.741 × 10⁹²(93-digit number)

27415960960537882549…36961359436589238799

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

2.741 × 10⁹²(93-digit number)

27415960960537882549…36961359436589238799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.741 × 10⁹²(93-digit number)

27415960960537882549…36961359436589238801

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

5.483 × 10⁹²(93-digit number)

54831921921075765098…73922718873178477599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.483 × 10⁹²(93-digit number)

54831921921075765098…73922718873178477601

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

1.096 × 10⁹³(94-digit number)

10966384384215153019…47845437746356955199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.096 × 10⁹³(94-digit number)

10966384384215153019…47845437746356955201

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

2.193 × 10⁹³(94-digit number)

21932768768430306039…95690875492713910399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.193 × 10⁹³(94-digit number)

21932768768430306039…95690875492713910401

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

4.386 × 10⁹³(94-digit number)

43865537536860612078…91381750985427820799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.386 × 10⁹³(94-digit number)

43865537536860612078…91381750985427820801

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 #193,986

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