Block #241,958

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 11/3/2013, 12:15:11 PM · Difficulty 9.9588 · 6,563,207 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

dfca6ebb1a8a27571bb7b3a300402e9543c4b445beedd14f41261375aedbdaa3

View on Chainz ↗

Height

#241,958

Difficulty

9.958794

Transactions

Size

799 B

Version

Bits

09f57385

Nonce

321,136

Timestamp

11/3/2013, 12:15:11 PM

Confirmations

6,563,207

Mined by

⛏️ P2SHAZ9gwDSQ9eWoQY9W5dUGn7b9Zwha77qwDk

Merkle Root

8944f6412ca88ffbd0b59e283763b5e36afd1dd22e88fd62026d57f7f338d1b7

Transactions (3)

Coinbasebf1af78232bf46…227b3679da5b17

1 in → 1 out10.0900 XPM109 B

AZ9gwDSQ…ha77qwDk

036231573b98d2…56137f8e20f1ad

2 in → 2 out20.1600 XPM375 B

AYJZB9uv…W7reky1H ASuoUi24…FwBoFbxd

36a9b8c3162f6b…7484dd036123c5

1 in → 2 out10.0700 XPM225 B

ANmGQNfJ…HxcmxbWJ AGeHdmmN…QDKvFMxW

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.

4.669 × 10⁹³(94-digit number)

46695887088987363214…93892216072075904159

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

4.669 × 10⁹³(94-digit number)

46695887088987363214…93892216072075904159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.669 × 10⁹³(94-digit number)

46695887088987363214…93892216072075904161

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

9.339 × 10⁹³(94-digit number)

93391774177974726428…87784432144151808319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.339 × 10⁹³(94-digit number)

93391774177974726428…87784432144151808321

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

1.867 × 10⁹⁴(95-digit number)

18678354835594945285…75568864288303616639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.867 × 10⁹⁴(95-digit number)

18678354835594945285…75568864288303616641

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

3.735 × 10⁹⁴(95-digit number)

37356709671189890571…51137728576607233279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.735 × 10⁹⁴(95-digit number)

37356709671189890571…51137728576607233281

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

7.471 × 10⁹⁴(95-digit number)

74713419342379781143…02275457153214466559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.471 × 10⁹⁴(95-digit number)

74713419342379781143…02275457153214466561

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

1.494 × 10⁹⁵(96-digit number)

14942683868475956228…04550914306428933119

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