Block #194,693

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/5/2013, 7:07:24 AM · Difficulty 9.8802 · 6,614,642 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8dc8a337b8ca2820a62c45665781b37ce3c1ec5ea40a84b813459a64a9d0d5b5

View on Chainz ↗

Height

#194,693

Difficulty

9.880154

Transactions

Size

3.80 KB

Version

Bits

09e151c9

Nonce

1,164,751,076

Timestamp

10/5/2013, 7:07:24 AM

Confirmations

6,614,642

Mined by

⛏️ ROAZ4gvP32JykZfxFxsUJ5CdKrA4ukKsCiYr

Merkle Root

7d0d6f4bd8e17d1bbd9346b33c91803678a11bfb75684060f957ab52a7be50d2

Transactions (1)

Coinbase7d0d6f4bd8e17d…57ab52a7be50d2

1 in → 110 out10.1900 XPM3.71 KB

AZ4gvP32…ukKsCiYr AcPkH5Yw…MM4Y9NNu Aabufq6z…vs9soDm5 AKRpbXWP…X6DRYUqb Ab7ULbjQ…fuVABZZs

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.

1.207 × 10⁹⁷(98-digit number)

12076107975071594083…72801983790442801619

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

1.207 × 10⁹⁷(98-digit number)

12076107975071594083…72801983790442801619

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.207 × 10⁹⁷(98-digit number)

12076107975071594083…72801983790442801621

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

2.415 × 10⁹⁷(98-digit number)

24152215950143188166…45603967580885603239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.415 × 10⁹⁷(98-digit number)

24152215950143188166…45603967580885603241

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

4.830 × 10⁹⁷(98-digit number)

48304431900286376332…91207935161771206479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.830 × 10⁹⁷(98-digit number)

48304431900286376332…91207935161771206481

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

9.660 × 10⁹⁷(98-digit number)

96608863800572752665…82415870323542412959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.660 × 10⁹⁷(98-digit number)

96608863800572752665…82415870323542412961

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

1.932 × 10⁹⁸(99-digit number)

19321772760114550533…64831740647084825919

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 #194,693

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