Block #1,608,464

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/31/2016, 6:09:15 PM · Difficulty 10.6096 · 5,222,828 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9ed8de431d9dab27d55c9efe23c0c8eeb5b5001a7c52b9845f0b4390f6623887

View on Chainz ↗

Height

#1,608,464

Difficulty

10.609551

Transactions

Size

1.21 KB

Version

Bits

0a9c0b8f

Nonce

1,305,464,089

Timestamp

5/31/2016, 6:09:15 PM

Confirmations

5,222,828

Mined by

⛏️ P2SHALW9BbxqdoQtqSnLJgNRBc3oSVbPXVB2b3

Merkle Root

9175a8299b7ecf385a9dc3361c5a1c4095b82fb25bb54b3359d367a8bdc6c37f

Transactions (2)

Coinbase395fd9472f6162…49b401203f95d9

1 in → 1 out8.8900 XPM109 B

ALW9Bbxq…bPXVB2b3

074467d3e054be…f7ac7a938a11f7

1 in → 26 out179.2942 XPM1.02 KB

AZ7bdUiQ…VWjibCPn AUKgazgS…4Jf8ku45 ARShFjBR…1trefTDb AKHb9FgM…MmttZ9gm AVbPDrE9…qY1ei75k

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.

1.043 × 10⁹⁷(98-digit number)

10439294334430632545…31257256430529576959

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

1.043 × 10⁹⁷(98-digit number)

10439294334430632545…31257256430529576959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.043 × 10⁹⁷(98-digit number)

10439294334430632545…31257256430529576961

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

2.087 × 10⁹⁷(98-digit number)

20878588668861265090…62514512861059153919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.087 × 10⁹⁷(98-digit number)

20878588668861265090…62514512861059153921

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

4.175 × 10⁹⁷(98-digit number)

41757177337722530181…25029025722118307839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.175 × 10⁹⁷(98-digit number)

41757177337722530181…25029025722118307841

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

8.351 × 10⁹⁷(98-digit number)

83514354675445060362…50058051444236615679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.351 × 10⁹⁷(98-digit number)

83514354675445060362…50058051444236615681

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

1.670 × 10⁹⁸(99-digit number)

16702870935089012072…00116102888473231359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.670 × 10⁹⁸(99-digit number)

16702870935089012072…00116102888473231361

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 #1,608,464

Cookie Preferences