Block #223,864

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/23/2013, 8:37:41 AM · Difficulty 9.9374 · 6,568,716 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

84fae956f7ad37d8de37bc68e6529de9216b0d793f88757a1e63a597c4893e50

View on Chainz ↗

Height

#223,864

Difficulty

9.937401

Transactions

Size

3.01 KB

Version

Bits

09eff98a

Nonce

131,778

Timestamp

10/23/2013, 8:37:41 AM

Confirmations

6,568,716

Merkle Root

bbf96b28c0bf6d5152f8670febc027e0cf5e4a16fb8ff5fc4810e033eae51d68

Transactions (3)

Coinbase0e7311795708d7…fac2ed6b755d39

1 in → 1 out10.1500 XPM109 B

ASgeTpCB…irGabHuH

810d697b687e2c…14dc1259c5f2cd

19 in → 1 out192.4600 XPM2.16 KB

AbxSykSg…BX71twYi

878be68123e7fa…ba520353b09e18

4 in → 2 out5.0252 XPM671 B

AZ5ywELK…rRaX7ayW AVYA5FSq…eeZm8KGY

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.

9.971 × 10⁹³(94-digit number)

99711016201361872962…39214696487968238079

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

9.971 × 10⁹³(94-digit number)

99711016201361872962…39214696487968238079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.971 × 10⁹³(94-digit number)

99711016201361872962…39214696487968238081

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

1.994 × 10⁹⁴(95-digit number)

19942203240272374592…78429392975936476159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.994 × 10⁹⁴(95-digit number)

19942203240272374592…78429392975936476161

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

3.988 × 10⁹⁴(95-digit number)

39884406480544749184…56858785951872952319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.988 × 10⁹⁴(95-digit number)

39884406480544749184…56858785951872952321

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

7.976 × 10⁹⁴(95-digit number)

79768812961089498369…13717571903745904639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.976 × 10⁹⁴(95-digit number)

79768812961089498369…13717571903745904641

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

1.595 × 10⁹⁵(96-digit number)

15953762592217899673…27435143807491809279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.595 × 10⁹⁵(96-digit number)

15953762592217899673…27435143807491809281

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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