Block #490,838

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/14/2014, 2:55:42 AM · Difficulty 10.6797 · 6,308,488 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

995da161e77316f2fe6c04c8f0431acc5bda427e47c91d6735cce828cb9a1f3a

View on Chainz ↗

Height

#490,838

Difficulty

10.679731

Transactions

Size

1.22 KB

Version

Bits

0aae02d2

Nonce

272,136,972

Timestamp

4/14/2014, 2:55:42 AM

Confirmations

6,308,488

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

085b606d6ef09cc169bd0c6cff4ea78d4f97d1de5e0a55759960e35c3ed27db6

Transactions (4)

Coinbased849469b4233a5…901ebc4948df82

1 in → 1 out8.7800 XPM116 B

AbwWkWZt…kawDhufa

6c742603778e94…cd62f4888253c9

2 in → 2 out13.0453 XPM374 B

AcBHcceC…CzvUjmET AMPoNWkF…38SJachn

359593602132a4…02a75b4406a96f

2 in → 5 out12.6402 XPM442 B

AL6zXFS5…LNL1HHAB AXHFnvkB…yXdZX2Fh AeKNrjNj…1NEq95Ta ATKhxLfh…K9DABVGm AcBvLaSu…X3gaHvJ1

7ee21bde2541cb…77ddeec8b14c41

1 in → 2 out1.8951 XPM225 B

ALqQ1RGo…XshfUGGc AUd7jifX…FEEpCDTV

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.

2.386 × 10⁹⁷(98-digit number)

23862832446843801611…17194511396698584389

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

2.386 × 10⁹⁷(98-digit number)

23862832446843801611…17194511396698584389

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.386 × 10⁹⁷(98-digit number)

23862832446843801611…17194511396698584391

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

4.772 × 10⁹⁷(98-digit number)

47725664893687603223…34389022793397168779

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.772 × 10⁹⁷(98-digit number)

47725664893687603223…34389022793397168781

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

9.545 × 10⁹⁷(98-digit number)

95451329787375206446…68778045586794337559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.545 × 10⁹⁷(98-digit number)

95451329787375206446…68778045586794337561

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

1.909 × 10⁹⁸(99-digit number)

19090265957475041289…37556091173588675119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.909 × 10⁹⁸(99-digit number)

19090265957475041289…37556091173588675121

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

3.818 × 10⁹⁸(99-digit number)

38180531914950082578…75112182347177350239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.818 × 10⁹⁸(99-digit number)

38180531914950082578…75112182347177350241

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