Block #229,760

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/27/2013, 9:23:40 AM · Difficulty 9.9386 · 6,569,524 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7a1e9f7e79f6ec08a56846c7956fed62342b353c7573468bb90f602ac7413a4b

View on Chainz ↗

Height

#229,760

Difficulty

9.938616

Transactions

Size

1.13 KB

Version

Bits

09f0491c

Nonce

236,590

Timestamp

10/27/2013, 9:23:40 AM

Confirmations

6,569,524

Mined by

⛏️ P2SHAXxMa99wmoTJL3xWXDWe2MaiqiHfRGJSA7

Merkle Root

6a26bb9ecb67b80e586080d93f0df7a53bf548fbaebff00fbc227486f55df140

Transactions (3)

Coinbaseb3b1adcc91f23f…c601e80f5b58fc

1 in → 1 out10.1300 XPM109 B

AXxMa99w…HfRGJSA7

3a04bddd1ca27c…206d61ac4c834c

6 in → 1 out60.7100 XPM727 B

ATV4M1CV…dd9zw8nH

4fd2483ee0af60…67ca2dbb5f96c4

1 in → 2 out3.4967 XPM227 B

AQnWMim4…qG8rjHWB AHqLzutR…LtNLWcHw

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.

1.668 × 10⁹⁴(95-digit number)

16686917728109182178…68243920908627726399

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

1.668 × 10⁹⁴(95-digit number)

16686917728109182178…68243920908627726399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.668 × 10⁹⁴(95-digit number)

16686917728109182178…68243920908627726401

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

3.337 × 10⁹⁴(95-digit number)

33373835456218364356…36487841817255452799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.337 × 10⁹⁴(95-digit number)

33373835456218364356…36487841817255452801

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

6.674 × 10⁹⁴(95-digit number)

66747670912436728713…72975683634510905599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.674 × 10⁹⁴(95-digit number)

66747670912436728713…72975683634510905601

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

1.334 × 10⁹⁵(96-digit number)

13349534182487345742…45951367269021811199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.334 × 10⁹⁵(96-digit number)

13349534182487345742…45951367269021811201

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

2.669 × 10⁹⁵(96-digit number)

26699068364974691485…91902734538043622399

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