Block #1,410,617

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/12/2016, 8:05:00 PM · Difficulty 10.8052 · 5,399,655 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

cbbc0af24f42b52feb6a9a94e6ad001fa0cc30af3a1fac4d9e1b30a130583ec0

View on Chainz ↗

Height

#1,410,617

Difficulty

10.805188

Transactions

Size

936 B

Version

Bits

0ace20cb

Nonce

184,744,976

Timestamp

1/12/2016, 8:05:00 PM

Confirmations

5,399,655

Mined by

⛏️ P2SHAFu779U1wrqtQzCZ73cnooXamLw3QZE745

Merkle Root

f1005431c8a09dca674bcb84bad675d632c376ecef9ca7a10a2b2fa4149fdb85

Transactions (2)

Coinbaseb0d1d3f38891d6…043deaa0ff830a

1 in → 1 out8.5600 XPM110 B

AFu779U1…w3QZE745

d5f7443722af79…74c28c2a2ec92b

1 in → 17 out43.0805 XPM735 B

AcbToZyq…pooyBoGx AdN1cPGQ…3WtjXRtv ARB6qyYM…UfzKMJj1 ATUW1u6X…YYAQqaKM ALeEWJaz…889pPtcR

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.

8.620 × 10⁹⁶(97-digit number)

86207274274305255999…51257278361755320319

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

8.620 × 10⁹⁶(97-digit number)

86207274274305255999…51257278361755320319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.620 × 10⁹⁶(97-digit number)

86207274274305255999…51257278361755320321

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

1.724 × 10⁹⁷(98-digit number)

17241454854861051199…02514556723510640639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.724 × 10⁹⁷(98-digit number)

17241454854861051199…02514556723510640641

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

3.448 × 10⁹⁷(98-digit number)

34482909709722102399…05029113447021281279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.448 × 10⁹⁷(98-digit number)

34482909709722102399…05029113447021281281

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

6.896 × 10⁹⁷(98-digit number)

68965819419444204799…10058226894042562559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.896 × 10⁹⁷(98-digit number)

68965819419444204799…10058226894042562561

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

1.379 × 10⁹⁸(99-digit number)

13793163883888840959…20116453788085125119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.379 × 10⁹⁸(99-digit number)

13793163883888840959…20116453788085125121

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 #1,410,617

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