Block #229,225

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/27/2013, 1:19:53 AM · Difficulty 9.9381 · 6,560,813 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

474c75eaeb084a0916cedcf473f742f91f3d79a6cdede06e61f26d104aa51cba

View on Chainz ↗

Height

#229,225

Difficulty

9.938086

Transactions

Size

1.08 KB

Version

Bits

09f02669

Nonce

139,137

Timestamp

10/27/2013, 1:19:53 AM

Confirmations

6,560,813

Merkle Root

4711f56f931a27a748e4187efb1a4b6a6ec1cc7d35790695fb68f06eff8a22f2

Transactions (5)

Coinbase2896e8238094c0…f8501ccc5b9abd

1 in → 1 out10.1500 XPM109 B

AJX1bfKn…FPgx2vAD

bb592c1d945e3e…071fb842e425d8

1 in → 2 out10.1000 XPM227 B

AUQpfajA…HZCDAwmH AdWp2YRv…FDtt217a

166564300afec7…a2af7ab2eebdc5

1 in → 2 out8.0509 XPM226 B

AeXSKXyB…3LVeYMHt Abu4RdWt…T8f8mYwe

2c8046544e574b…cf99dd7c3f55c6

1 in → 2 out6.8078 XPM226 B

ASnSjgQg…fewAaNPL AHpkMdzs…e6Vv4vPz

5cbafd25d2935f…2867c5e0cd1111

1 in → 2 out6.5529 XPM227 B

AN3QK9wE…SHQv3wVg AQjC9wux…GS3xHbBe

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.

2.219 × 10⁹¹(92-digit number)

22191887721450443816…83058937482245468159

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

2.219 × 10⁹¹(92-digit number)

22191887721450443816…83058937482245468159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.219 × 10⁹¹(92-digit number)

22191887721450443816…83058937482245468161

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

4.438 × 10⁹¹(92-digit number)

44383775442900887633…66117874964490936319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.438 × 10⁹¹(92-digit number)

44383775442900887633…66117874964490936321

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

8.876 × 10⁹¹(92-digit number)

88767550885801775267…32235749928981872639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.876 × 10⁹¹(92-digit number)

88767550885801775267…32235749928981872641

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

1.775 × 10⁹²(93-digit number)

17753510177160355053…64471499857963745279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.775 × 10⁹²(93-digit number)

17753510177160355053…64471499857963745281

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

3.550 × 10⁹²(93-digit number)

35507020354320710107…28942999715927490559

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