Block #507,415

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/23/2014, 5:36:03 PM · Difficulty 10.8161 · 6,300,651 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f75fd993c5d455fd7be1881ae551235d2c3369aefd3f7b1eca0789641a5f1fa1

View on Chainz ↗

Height

#507,415

Difficulty

10.816065

Transactions

Size

1.83 KB

Version

Bits

0ad0e9a4

Nonce

734,126,207

Timestamp

4/23/2014, 5:36:03 PM

Confirmations

6,300,651

Mined by

⛏️ P2SHATqy4obzqa9rCbt3LuWRkPp7KBcGuYobc3

Merkle Root

6153f6f4d260fb535448b35925329838e691dc2dbe65273f2085a356fb40079f

Transactions (5)

Coinbase2a39257018f76c…e209cc453a3e97

1 in → 1 out8.5700 XPM109 B

ATqy4obz…cGuYobc3

2727ad5ee5d91d…9b785c3cd1047d

5 in → 4 out9.4074 XPM853 B

AeKNrjNj…1NEq95Ta AVBgdTW6…6N4QfJBJ AVMRAzar…3e1KTuWa AHbu8w6V…13P7BwSQ

2a5061d3925c2c…2d3e1284a1c4f8

1 in → 2 out4.4863 XPM226 B

Ac1giiPz…YxmH5ksS AcdyemUU…wyL11368

c6e64d6c36d594…f2812c6017c3cf

1 in → 2 out2.5391 XPM226 B

AHHg3hqQ…BCkNwxyd ATrAhzR8…tFwprQ2C

d0d1928760adc7…9d8a75a454d0cb

2 in → 2 out4.3339 XPM375 B

ANz1tuDW…qpCw4eHg Aeibw7eB…DXww2mo2

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.

1.663 × 10⁹⁰(91-digit number)

16632947472825727533…90563851059408309359

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

1.663 × 10⁹⁰(91-digit number)

16632947472825727533…90563851059408309359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.663 × 10⁹⁰(91-digit number)

16632947472825727533…90563851059408309361

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

3.326 × 10⁹⁰(91-digit number)

33265894945651455066…81127702118816618719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.326 × 10⁹⁰(91-digit number)

33265894945651455066…81127702118816618721

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

6.653 × 10⁹⁰(91-digit number)

66531789891302910133…62255404237633237439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.653 × 10⁹⁰(91-digit number)

66531789891302910133…62255404237633237441

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

1.330 × 10⁹¹(92-digit number)

13306357978260582026…24510808475266474879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.330 × 10⁹¹(92-digit number)

13306357978260582026…24510808475266474881

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

2.661 × 10⁹¹(92-digit number)

26612715956521164053…49021616950532949759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.661 × 10⁹¹(92-digit number)

26612715956521164053…49021616950532949761

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 #507,415

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