Block #212,946

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/16/2013, 2:47:14 PM · Difficulty 9.9197 · 6,595,191 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7c8438b63d6c4478ffd619b557610c436756e694d007911042b68f615a06d028

View on Chainz ↗

Height

#212,946

Difficulty

9.919730

Transactions

Size

1.29 KB

Version

Bits

09eb7366

Nonce

135,665

Timestamp

10/16/2013, 2:47:14 PM

Confirmations

6,595,191

Mined by

⛏️ P2SHAdri1peAughZq8G5PLQwx2WYB3DAdav5HF

Merkle Root

1fda96865dade108cbe9978ff5f02367b8e2b6e222b2d48f1d2b22548af42e9c

Transactions (4)

Coinbase5477ec4170b6c6…9980d06343aac9

1 in → 1 out10.1800 XPM109 B

Adri1peA…DAdav5HF

fec12bf8233b21…e088971281b9dc

4 in → 2 out11.2742 XPM673 B

AKpJAnxS…r7K9LYXH ASuoUi24…FwBoFbxd

9fab605cde9aa4…c2e35a14bfa211

1 in → 2 out8.0878 XPM227 B

ATRp3y4y…xxApfdEh AUUJC7ne…cmZaPWM6

1342ab0b0545dc…5f9d3b774051c2

1 in → 2 out6.0724 XPM227 B

AHdBEbcD…aeRBHTTD AHBP8Zu5…o3ABnCec

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.

1.331 × 10⁹¹(92-digit number)

13312294499444080335…09214092675988737199

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

1.331 × 10⁹¹(92-digit number)

13312294499444080335…09214092675988737199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.331 × 10⁹¹(92-digit number)

13312294499444080335…09214092675988737201

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

2.662 × 10⁹¹(92-digit number)

26624588998888160670…18428185351977474399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.662 × 10⁹¹(92-digit number)

26624588998888160670…18428185351977474401

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

5.324 × 10⁹¹(92-digit number)

53249177997776321341…36856370703954948799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.324 × 10⁹¹(92-digit number)

53249177997776321341…36856370703954948801

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

1.064 × 10⁹²(93-digit number)

10649835599555264268…73712741407909897599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.064 × 10⁹²(93-digit number)

10649835599555264268…73712741407909897601

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

2.129 × 10⁹²(93-digit number)

21299671199110528536…47425482815819795199

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 #212,946

Cookie Preferences