Block #233,527

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/29/2013, 6:54:27 PM · Difficulty 9.9426 · 6,570,266 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e1ad3e847c3efd12a671ac318ad843a9b7ad5379bd24dd056689ab9237da3c3d

View on Chainz ↗

Height

#233,527

Difficulty

9.942640

Transactions

Size

2.67 KB

Version

Bits

09f150e1

Nonce

88,604

Timestamp

10/29/2013, 6:54:27 PM

Confirmations

6,570,266

Mined by

⛏️ P2SHARYq5Dturq4TgdmQ4UfSVxbHdaSy61b4yF

Merkle Root

ffa6a4a66e425110716614fdd42d4e74182fc15cbf80ceeda1c439d0a7a80588

Transactions (5)

Coinbasedb228ff827453c…90bed92936c225

1 in → 1 out10.1500 XPM109 B

ARYq5Dtu…Sy61b4yF

f9b4cb4b329719…a16eebfbb27244

11 in → 2 out100.0788 XPM1.67 KB

AJUyBcjg…5QhUeA6v ALZ9xdgF…iWNNFb5H

6ff5099b5fed8a…88c8572f9632f8

1 in → 2 out10.1000 XPM225 B

APXFRUjc…epQMJwCk AYKVeNA9…BbJrTDhi

573bbbdf70f707…24369ae3575e0b

1 in → 2 out5.9896 XPM225 B

AXCCsfyG…SSSFr1ZK AQLNrVHM…honSQzni

3c238f471ee003…0cad305503b8f3

2 in → 2 out2.0754 XPM374 B

AHqWCiSE…oLQrNAqG AYBs9UTC…odqRGSpW

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.

3.178 × 10⁹³(94-digit number)

31784748812295554720…54426981583155836799

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

3.178 × 10⁹³(94-digit number)

31784748812295554720…54426981583155836799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.178 × 10⁹³(94-digit number)

31784748812295554720…54426981583155836801

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

6.356 × 10⁹³(94-digit number)

63569497624591109440…08853963166311673599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.356 × 10⁹³(94-digit number)

63569497624591109440…08853963166311673601

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

1.271 × 10⁹⁴(95-digit number)

12713899524918221888…17707926332623347199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.271 × 10⁹⁴(95-digit number)

12713899524918221888…17707926332623347201

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

2.542 × 10⁹⁴(95-digit number)

25427799049836443776…35415852665246694399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.542 × 10⁹⁴(95-digit number)

25427799049836443776…35415852665246694401

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

5.085 × 10⁹⁴(95-digit number)

50855598099672887552…70831705330493388799

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