Block #498,984

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/18/2014, 9:09:08 AM · Difficulty 10.7864 · 6,318,415 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c226c80de232c76026b9cfc925b469f99443f502a4448ce2e5c2dbaa8e827da1

View on Chainz ↗

Height

#498,984

Difficulty

10.786401

Transactions

Size

833 B

Version

Bits

0ac9519b

Nonce

52,674

Timestamp

4/18/2014, 9:09:08 AM

Confirmations

6,318,415

Mined by

⛏️ aSPAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

faedae101b36700b60583c9f06704e1c6ba7853b826c91abee34a362a50d0ac4

Transactions (1)

Coinbasefaedae101b3670…34a362a50d0ac4

1 in → 20 out8.5800 XPM743 B

AQvZBsUo…hppgRZTJ ANNg88pG…ppn21sTe ATKK7iFz…wZm46KN1 AJtNW28X…Syb4Ph5j AUbecsVa…i8zo8qRf

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.

3.514 × 10⁹⁴(95-digit number)

35144091252880759828…64022550742411396479

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

3.514 × 10⁹⁴(95-digit number)

35144091252880759828…64022550742411396479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.514 × 10⁹⁴(95-digit number)

35144091252880759828…64022550742411396481

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

7.028 × 10⁹⁴(95-digit number)

70288182505761519656…28045101484822792959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.028 × 10⁹⁴(95-digit number)

70288182505761519656…28045101484822792961

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

1.405 × 10⁹⁵(96-digit number)

14057636501152303931…56090202969645585919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.405 × 10⁹⁵(96-digit number)

14057636501152303931…56090202969645585921

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

2.811 × 10⁹⁵(96-digit number)

28115273002304607862…12180405939291171839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.811 × 10⁹⁵(96-digit number)

28115273002304607862…12180405939291171841

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

5.623 × 10⁹⁵(96-digit number)

56230546004609215725…24360811878582343679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.623 × 10⁹⁵(96-digit number)

56230546004609215725…24360811878582343681

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 #498,984

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