Block #244,348

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/4/2013, 7:43:26 PM · Difficulty 9.9628 · 6,564,666 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e9b4a7e00407a265b7ca26d71ede307c94c16ad9a5ad511ec96a7ced99ee6f1d

View on Chainz ↗

Height

#244,348

Difficulty

9.962793

Transactions

Size

1.93 KB

Version

Bits

09f6799f

Nonce

41,051

Timestamp

11/4/2013, 7:43:26 PM

Confirmations

6,564,666

Mined by

⛏️ P2SHAHhQ1C5qyWQfuChtznhujjDyLdcWtxGvVx

Merkle Root

92412e22bfe6086b13e47ed968fc1e38601da016512e59e986d4cd167882672f

Transactions (3)

Coinbasef7906e2db7df08…83bece8f4c34fe

1 in → 1 out10.0900 XPM109 B

AHhQ1C5q…cWtxGvVx

1478a3a2376391…42f54700738dd7

2 in → 2 out70.0120 XPM374 B

AP1RztWs…Fbw3v2Mw ANu1uQmH…FzivVjnt

a7bf459c3fc541…e67f6dd83a65a4

9 in → 2 out3.0326 XPM1.38 KB

ARitzeAs…zBHrD3ss AeKNrjNj…1NEq95Ta

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.

3.314 × 10⁹⁴(95-digit number)

33147568307809376222…53477336157157445679

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

3.314 × 10⁹⁴(95-digit number)

33147568307809376222…53477336157157445679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.314 × 10⁹⁴(95-digit number)

33147568307809376222…53477336157157445681

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

6.629 × 10⁹⁴(95-digit number)

66295136615618752445…06954672314314891359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.629 × 10⁹⁴(95-digit number)

66295136615618752445…06954672314314891361

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

1.325 × 10⁹⁵(96-digit number)

13259027323123750489…13909344628629782719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.325 × 10⁹⁵(96-digit number)

13259027323123750489…13909344628629782721

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

2.651 × 10⁹⁵(96-digit number)

26518054646247500978…27818689257259565439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.651 × 10⁹⁵(96-digit number)

26518054646247500978…27818689257259565441

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

5.303 × 10⁹⁵(96-digit number)

53036109292495001956…55637378514519130879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.303 × 10⁹⁵(96-digit number)

53036109292495001956…55637378514519130881

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 #244,348

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