Block #268,182

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/21/2013, 9:52:57 PM · Difficulty 9.9578 · 6,539,384 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

47ca0fb8de1335e379f8cee477da7add7c8cb4370b214b6b1f3851f32a4df056

View on Chainz ↗

Height

#268,182

Difficulty

9.957801

Transactions

Size

2.24 KB

Version

Bits

09f53275

Nonce

120,016

Timestamp

11/21/2013, 9:52:57 PM

Confirmations

6,539,384

Mined by

⛏️ P2SHAdGRRh1eP4JFvQMqy7y2pLsryDQmctLb24

Merkle Root

65c12346a6b7608394a6d6f4a2b47796ec5241139cb99dc652827f6b34c2ae0d

Transactions (5)

Coinbasede910e0fdfc0e8…0c5c014cd891d7

1 in → 2 out10.1100 XPM141 B

AdGRRh1e…QmctLb24 Abiw8n3q…ZnZfgvQW

47639a8dd7c0aa…694985d01a8081

4 in → 2 out1500.0100 XPM672 B

AQwHq3Z4…ggMcfddP AeXmns4M…hoUzVhXB

d96431c5dd30d7…808648524124d6

2 in → 1 out20.0000 XPM339 B

AVfpR6CL…sCivMRWH

1b0d83987ee81c…0054027fe9f233

2 in → 2 out142.7331 XPM374 B

AbZymyRQ…YZm38rjw AUe7L1eo…7UJ6qYHs

bf2b9635eb1997…3c8ae1f2c6afec

4 in → 2 out69.5535 XPM670 B

AP3oAe4W…H9paTkCm AS2Sa8j5…zuMmYj4Q

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.

4.088 × 10¹⁰³(104-digit number)

40888353596487461669…67745753700742023999

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

4.088 × 10¹⁰³(104-digit number)

40888353596487461669…67745753700742023999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.088 × 10¹⁰³(104-digit number)

40888353596487461669…67745753700742024001

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

8.177 × 10¹⁰³(104-digit number)

81776707192974923339…35491507401484047999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.177 × 10¹⁰³(104-digit number)

81776707192974923339…35491507401484048001

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

1.635 × 10¹⁰⁴(105-digit number)

16355341438594984667…70983014802968095999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.635 × 10¹⁰⁴(105-digit number)

16355341438594984667…70983014802968096001

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

3.271 × 10¹⁰⁴(105-digit number)

32710682877189969335…41966029605936191999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.271 × 10¹⁰⁴(105-digit number)

32710682877189969335…41966029605936192001

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

6.542 × 10¹⁰⁴(105-digit number)

65421365754379938671…83932059211872383999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.542 × 10¹⁰⁴(105-digit number)

65421365754379938671…83932059211872384001

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

Block #268,182

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