Block #195,140

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/5/2013, 2:44:20 PM · Difficulty 9.8801 · 6,622,114 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b12fed71a9b7d4629574526b366628e1a231371838e0c4aa1d5b8488eff37a39

View on Chainz ↗

Height

#195,140

Difficulty

9.880061

Transactions

Size

650 B

Version

Bits

09e14bb2

Nonce

311,185

Timestamp

10/5/2013, 2:44:20 PM

Confirmations

6,622,114

Mined by

⛏️ P2SHAb46SiTBPeSDhuwnTmimSkwkD6NAVJuHUW

Merkle Root

14c6c1a50d1e06e74beec9a2772c71ac1c5d51c3abbc006898ad67fe68b14e4d

Transactions (3)

Coinbasebeb8d76ad46c9d…26683b124d6ed3

1 in → 1 out10.2500 XPM109 B

Ab46SiTB…NAVJuHUW

ba7457eaf2d883…ff415da43fc3ae

1 in → 2 out4.1743 XPM225 B

AeEcSGAf…HjtsPDKX AVjuS95J…3jZhSSxh

c45ab0657a4e8a…7213c8ee8c33fb

1 in → 2 out3.1376 XPM227 B

ATwKBEVF…QFZamrLX ANShBaCx…NttHiwPk

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.

9.318 × 10⁹²(93-digit number)

93188410679913724108…49862760042962609899

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

9.318 × 10⁹²(93-digit number)

93188410679913724108…49862760042962609899

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.318 × 10⁹²(93-digit number)

93188410679913724108…49862760042962609901

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

1.863 × 10⁹³(94-digit number)

18637682135982744821…99725520085925219799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.863 × 10⁹³(94-digit number)

18637682135982744821…99725520085925219801

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

3.727 × 10⁹³(94-digit number)

37275364271965489643…99451040171850439599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.727 × 10⁹³(94-digit number)

37275364271965489643…99451040171850439601

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

7.455 × 10⁹³(94-digit number)

74550728543930979286…98902080343700879199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.455 × 10⁹³(94-digit number)

74550728543930979286…98902080343700879201

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

1.491 × 10⁹⁴(95-digit number)

14910145708786195857…97804160687401758399

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 #195,140

Cookie Preferences