Block #499,538

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/18/2014, 4:11:31 PM · Difficulty 10.7920 · 6,317,212 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

84de6994ce9abed9ed49e283f2bb8b2cfdb05a81096cc6d9b9081a2128064c80

View on Chainz ↗

Height

#499,538

Difficulty

10.791959

Transactions

Size

765 B

Version

Bits

0acabdd5

Nonce

8,119

Timestamp

4/18/2014, 4:11:31 PM

Confirmations

6,317,212

Mined by

⛏️ RaSQN":AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

9a06a13e14cd9fcdad0f471af367f165f413aa72a547cdc7ad1b31790a21e1ab

Transactions (1)

Coinbase9a06a13e14cd9f…1b31790a21e1ab

1 in → 18 out8.5700 XPM675 B

AQvZBsUo…hppgRZTJ ANNg88pG…ppn21sTe AdxPNkWD…ZMa9u34q ATKK7iFz…wZm46KN1 AJtNW28X…Syb4Ph5j

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.

2.775 × 10⁹⁵(96-digit number)

27752246373895227076…55470912652265279999

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

2.775 × 10⁹⁵(96-digit number)

27752246373895227076…55470912652265279999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.775 × 10⁹⁵(96-digit number)

27752246373895227076…55470912652265280001

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

5.550 × 10⁹⁵(96-digit number)

55504492747790454152…10941825304530559999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.550 × 10⁹⁵(96-digit number)

55504492747790454152…10941825304530560001

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

1.110 × 10⁹⁶(97-digit number)

11100898549558090830…21883650609061119999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.110 × 10⁹⁶(97-digit number)

11100898549558090830…21883650609061120001

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

2.220 × 10⁹⁶(97-digit number)

22201797099116181660…43767301218122239999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.220 × 10⁹⁶(97-digit number)

22201797099116181660…43767301218122240001

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

4.440 × 10⁹⁶(97-digit number)

44403594198232363321…87534602436244479999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.440 × 10⁹⁶(97-digit number)

44403594198232363321…87534602436244480001

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 #499,538

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