Block #211,577

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/15/2013, 7:02:24 PM · Difficulty 9.9167 · 6,581,939 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

cc9c9b56f7f5b21b5af272696d496db50d91b15cef5a7e5adedf6794a361cc11

View on Chainz ↗

Height

#211,577

Difficulty

9.916662

Transactions

Size

547 B

Version

Bits

09eaaa5f

Nonce

218

Timestamp

10/15/2013, 7:02:24 PM

Confirmations

6,581,939

Merkle Root

f978e5504d109bfe6dcf6466484270da9753f330378b384902ec54e6970f6da3

Transactions (3)

Coinbasebe10a3edd95d02…979bc617a5f50d

1 in → 1 out10.1700 XPM109 B

AUMvgbAA…tcTnrzh9

b952fc744e4971…b4c64481fb7d56

1 in → 1 out10.1700 XPM157 B

AKVZmjFY…iuD64V6a

c7ef1caa3eede3…d235779d0e9d7a

1 in → 2 out10.1700 XPM192 B

ATLj2fSQ…fu1GBKxe AQAvQSWZ…C9mFkvux

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.

5.084 × 10⁹¹(92-digit number)

50843952460733901323…83365639230174226219

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

5.084 × 10⁹¹(92-digit number)

50843952460733901323…83365639230174226219

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.084 × 10⁹¹(92-digit number)

50843952460733901323…83365639230174226221

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

1.016 × 10⁹²(93-digit number)

10168790492146780264…66731278460348452439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.016 × 10⁹²(93-digit number)

10168790492146780264…66731278460348452441

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

2.033 × 10⁹²(93-digit number)

20337580984293560529…33462556920696904879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.033 × 10⁹²(93-digit number)

20337580984293560529…33462556920696904881

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

4.067 × 10⁹²(93-digit number)

40675161968587121058…66925113841393809759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.067 × 10⁹²(93-digit number)

40675161968587121058…66925113841393809761

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

8.135 × 10⁹²(93-digit number)

81350323937174242117…33850227682787619519

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