Block #500,909

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/19/2014, 11:07:10 AM · Difficulty 10.8018 · 6,307,228 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

59b9e56b361659b8b791182d0413b62ef80be098e18eef367eda622c360598a1

View on Chainz ↗

Height

#500,909

Difficulty

10.801829

Transactions

Size

3.21 KB

Version

Bits

0acd44a8

Nonce

90,892

Timestamp

4/19/2014, 11:07:10 AM

Confirmations

6,307,228

Mined by

⛏️ aSRX#$AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

84b7ec049f952efdaebece51ae4f31feae898f47e86b76cad31c73aff4bd07fc

Transactions (2)

Coinbase0336eed0f6df65…7d1f1ad073d0b8

1 in → 20 out8.5600 XPM743 B

AQvZBsUo…hppgRZTJ ANNg88pG…ppn21sTe AdxPNkWD…ZMa9u34q AUbecsVa…i8zo8qRf ATKK7iFz…wZm46KN1

4bdc45566368fc…93ae124c757daf

16 in → 2 out80.1811 XPM2.39 KB

Ad93hpdY…SQR8mj9g AYd3abw4…RFg7RdgF

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.

4.556 × 10¹⁰³(104-digit number)

45564890589324619758…84114823833723814399

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

4.556 × 10¹⁰³(104-digit number)

45564890589324619758…84114823833723814399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.556 × 10¹⁰³(104-digit number)

45564890589324619758…84114823833723814401

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

9.112 × 10¹⁰³(104-digit number)

91129781178649239517…68229647667447628799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.112 × 10¹⁰³(104-digit number)

91129781178649239517…68229647667447628801

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

1.822 × 10¹⁰⁴(105-digit number)

18225956235729847903…36459295334895257599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.822 × 10¹⁰⁴(105-digit number)

18225956235729847903…36459295334895257601

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

3.645 × 10¹⁰⁴(105-digit number)

36451912471459695806…72918590669790515199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.645 × 10¹⁰⁴(105-digit number)

36451912471459695806…72918590669790515201

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

7.290 × 10¹⁰⁴(105-digit number)

72903824942919391613…45837181339581030399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.290 × 10¹⁰⁴(105-digit number)

72903824942919391613…45837181339581030401

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 #500,909

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