Block #223,514

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/23/2013, 2:08:30 AM · Difficulty 9.9379 · 6,571,919 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

21cde02f0640044fa21d634aad7f5e6f36c4a1be8cd9b8ad0da904b89c1ee96c

View on Chainz ↗

Height

#223,514

Difficulty

9.937878

Transactions

Size

8.76 KB

Version

Bits

09f018c8

Nonce

169,348

Timestamp

10/23/2013, 2:08:30 AM

Confirmations

6,571,919

Mined by

⛏️ P2SHARaPyHgjo2zpePAfC2xk8aeQGMnA9veLYH

Merkle Root

a1abf59a5b117176210c4391acf7f11f08616515c9c8460d9382dc40c1a3655f

Transactions (3)

Coinbase99b7b9a4fea11b…dce9cdfe4e2a4f

1 in → 1 out10.2000 XPM109 B

ARaPyHgj…nA9veLYH

b72ae4f69ce177…fbd193ba17a841

24 in → 1 out243.5800 XPM2.72 KB

AY1cGaxZ…WikBH84c

6177cfa89b3e48…2fe5a4025f184f

40 in → 2 out300.0100 XPM5.85 KB

AKRSSL7b…EctyUv1W ASM9m1d7…Emo8QBmJ

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.

2.408 × 10⁹¹(92-digit number)

24089719583245976215…37099604573500738919

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

2.408 × 10⁹¹(92-digit number)

24089719583245976215…37099604573500738919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.408 × 10⁹¹(92-digit number)

24089719583245976215…37099604573500738921

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

4.817 × 10⁹¹(92-digit number)

48179439166491952430…74199209147001477839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.817 × 10⁹¹(92-digit number)

48179439166491952430…74199209147001477841

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

9.635 × 10⁹¹(92-digit number)

96358878332983904861…48398418294002955679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.635 × 10⁹¹(92-digit number)

96358878332983904861…48398418294002955681

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

1.927 × 10⁹²(93-digit number)

19271775666596780972…96796836588005911359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.927 × 10⁹²(93-digit number)

19271775666596780972…96796836588005911361

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

3.854 × 10⁹²(93-digit number)

38543551333193561944…93593673176011822719

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