Block #194,446

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/5/2013, 3:24:54 AM · Difficulty 9.8795 · 6,614,721 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d95d2a7fec1779186fe4dfa7c623833428c6799eb1adcc41ccf31d4442c845af

View on Chainz ↗

Height

#194,446

Difficulty

9.879486

Transactions

Size

1.16 KB

Version

Bits

09e125fb

Nonce

367,670

Timestamp

10/5/2013, 3:24:54 AM

Confirmations

6,614,721

Mined by

⛏️ P2SHANDqQMExdE8XT3Crihqv23NuvTAAmWQbv8

Merkle Root

8271a2e9f1e4590517794eee561ab595daa8edcd77bff830ff2809ce0e8387c4

Transactions (5)

Coinbasef61bcbfd9864a8…97dcccce80da00

1 in → 1 out10.2700 XPM109 B

ANDqQMEx…AAmWQbv8

75c14c1bad9ae5…7a7c256e69732b

1 in → 1 out10.2500 XPM157 B

AerEm8nA…cxuSKbey

198d7cb08ae07c…1f0b3d85b04ad7

1 in → 2 out10.2300 XPM226 B

ASuoUi24…FwBoFbxd ALxPACN1…qmKbQQ5R

8d3725147a5dd6…4bdf1d556012d8

1 in → 2 out7.2598 XPM226 B

AM97fKN6…EsLLdrr8 AbkuBBVh…fojLj8yS

01f30fc3c28ce0…eb54d9119b972c

2 in → 2 out6.1187 XPM374 B

ALQpdNVM…FfAFenvd AN3QK9wE…SHQv3wVg

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.

1.187 × 10⁹⁶(97-digit number)

11872475135648127090…34415914650229301999

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

1.187 × 10⁹⁶(97-digit number)

11872475135648127090…34415914650229301999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.187 × 10⁹⁶(97-digit number)

11872475135648127090…34415914650229302001

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

2.374 × 10⁹⁶(97-digit number)

23744950271296254181…68831829300458603999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.374 × 10⁹⁶(97-digit number)

23744950271296254181…68831829300458604001

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

4.748 × 10⁹⁶(97-digit number)

47489900542592508363…37663658600917207999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.748 × 10⁹⁶(97-digit number)

47489900542592508363…37663658600917208001

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

9.497 × 10⁹⁶(97-digit number)

94979801085185016726…75327317201834415999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.497 × 10⁹⁶(97-digit number)

94979801085185016726…75327317201834416001

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

1.899 × 10⁹⁷(98-digit number)

18995960217037003345…50654634403668831999

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 #194,446

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