Block #268,136

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 11/21/2013, 9:04:52 PM · Difficulty 9.9578 · 6,538,491 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8efbf4a3caf9067e85c71a316cb9567acdfb768025533c869a9d7d950e648db7

View on Chainz ↗

Height

#268,136

Difficulty

9.957836

Transactions

Size

1.43 KB

Version

Bits

09f534bf

Nonce

50,499

Timestamp

11/21/2013, 9:04:52 PM

Confirmations

6,538,491

Mined by

⛏️ P2SHAKcbk49N7DP3nse7MJr3Ed6rZiGJbKa7j1

Merkle Root

61eaabf59be23fb8643d8181fa13e32cfdadbcadaecd4d877eb6adcd98cafcfd

Transactions (4)

Coinbasee15422e762824b…2b022903e888f6

1 in → 2 out10.1000 XPM142 B

AKcbk49N…GJbKa7j1 AKNbfPoc…jfkpwAyL

c5c4d716d3c006…82fe00cc212c7b

2 in → 1 out159.9900 XPM338 B

ALEsSa9L…At5QqN7C

f0352b285d9dc0…03be4ce7956ff7

1 in → 2 out10.0200 XPM226 B

AQG6Azug…ZHNXEWdH AcHgGEW4…JhM8zLjt

74f193e74ad65c…77ca1104b65b95

4 in → 2 out26.8478 XPM668 B

AXUjoW7f…vyY8K4Pi AN7ZnJS4…uHpiPac9

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.

4.422 × 10¹⁰²(103-digit number)

44226748820713851017…74679016554958748799

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

4.422 × 10¹⁰²(103-digit number)

44226748820713851017…74679016554958748799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.422 × 10¹⁰²(103-digit number)

44226748820713851017…74679016554958748801

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

8.845 × 10¹⁰²(103-digit number)

88453497641427702035…49358033109917497599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.845 × 10¹⁰²(103-digit number)

88453497641427702035…49358033109917497601

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

1.769 × 10¹⁰³(104-digit number)

17690699528285540407…98716066219834995199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.769 × 10¹⁰³(104-digit number)

17690699528285540407…98716066219834995201

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

3.538 × 10¹⁰³(104-digit number)

35381399056571080814…97432132439669990399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.538 × 10¹⁰³(104-digit number)

35381399056571080814…97432132439669990401

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

7.076 × 10¹⁰³(104-digit number)

70762798113142161628…94864264879339980799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.076 × 10¹⁰³(104-digit number)

70762798113142161628…94864264879339980801

Verify on FactorDB ↗Wolfram Alpha ↗

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

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

1.415 × 10¹⁰⁴(105-digit number)

14152559622628432325…89728529758679961599

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #268,136

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