Block #191,150

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/2/2013, 10:48:38 PM · Difficulty 9.8756 · 6,612,329 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

cee8fda6ceb038e9b3bc61cbddfe943258c7a4075241abb3c673968c1bc8af9f

View on Chainz ↗

Height

#191,150

Difficulty

9.875647

Transactions

Size

1.08 KB

Version

Bits

09e02a65

Nonce

53,977

Timestamp

10/2/2013, 10:48:38 PM

Confirmations

6,612,329

Mined by

⛏️ P2SHAWeJ5Z1fpVJ9QX7VQp7ZRGG4BvVYZCgPXj

Merkle Root

4a461bca93022a80a801134f2ae4fade3f1e73db374188ca1c3b2d741ed1e1fb

Transactions (5)

Coinbase2748bfe07eb665…90e6574b60117d

1 in → 1 out10.2800 XPM109 B

AWeJ5Z1f…VYZCgPXj

ebac04010ce3b4…894c2b5f8ace20

1 in → 2 out10.2400 XPM226 B

AGQqTUwz…WBBDRasb AQnWMim4…qG8rjHWB

d2edf7c756c1da…deaec9353c58fc

1 in → 2 out10.2400 XPM226 B

AXgyKAKk…n5igALUy AQvLurSP…hSwACQyC

12c0a52a747469…cb85e14ef4592a

1 in → 2 out10.2400 XPM226 B

Af5xASA7…PKBm17io APfnkyGJ…rue7ZTJD

42133d04dddfe3…b134fb662eac87

1 in → 2 out5.6163 XPM225 B

AY2nLUvn…Gqx9Jn3z AMmGeXac…8N1iWEtv

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.

1.893 × 10⁹²(93-digit number)

18937768470701912607…24408548782253797069

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

1.893 × 10⁹²(93-digit number)

18937768470701912607…24408548782253797069

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.893 × 10⁹²(93-digit number)

18937768470701912607…24408548782253797071

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

3.787 × 10⁹²(93-digit number)

37875536941403825214…48817097564507594139

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.787 × 10⁹²(93-digit number)

37875536941403825214…48817097564507594141

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

7.575 × 10⁹²(93-digit number)

75751073882807650429…97634195129015188279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.575 × 10⁹²(93-digit number)

75751073882807650429…97634195129015188281

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

1.515 × 10⁹³(94-digit number)

15150214776561530085…95268390258030376559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.515 × 10⁹³(94-digit number)

15150214776561530085…95268390258030376561

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

3.030 × 10⁹³(94-digit number)

30300429553123060171…90536780516060753119

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