Block #76,414

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/22/2013, 12:27:48 AM · Difficulty 9.0961 · 6,714,578 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

411c4cc5f46dce944f631fd86de84cec93e294b6d33d937e243206734b294ee2

View on Chainz ↗

Height

#76,414

Difficulty

9.096052

Transactions

Size

1.37 KB

Version

Bits

091896e5

Nonce

494

Timestamp

7/22/2013, 12:27:48 AM

Confirmations

6,714,578

Merkle Root

ed97c5cd3c16e0912d2e731dbefbea0c927dc34808b3c9bc2650e78af25a6a3e

Transactions (4)

Coinbase2982a2d8f9cce8…0ae6148efd075b

1 in → 1 out12.1000 XPM110 B

AG9SDgRw…mb5kDRWy

ac915d14311139…5760ad56e7a000

1 in → 2 out61.9900 XPM227 B

AJaVWLcX…5uVGsFB5 ARcuWsh8…BigQyhiT

f3a8a991bd5fe8…e843de514173bd

5 in → 2 out410.1289 XPM819 B

AX9pMYcs…4HFYVJDX AGoj9nvR…UAHydaqS

ee1d85eb5278d7…5a1bbe63474073

1 in → 1 out12.3700 XPM158 B

AGFPbfsZ…CGTeoSvr

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.

6.507 × 10⁹⁸(99-digit number)

65073924608701845569…67745519875249246599

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

6.507 × 10⁹⁸(99-digit number)

65073924608701845569…67745519875249246599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.507 × 10⁹⁸(99-digit number)

65073924608701845569…67745519875249246601

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

1.301 × 10⁹⁹(100-digit number)

13014784921740369113…35491039750498493199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.301 × 10⁹⁹(100-digit number)

13014784921740369113…35491039750498493201

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

2.602 × 10⁹⁹(100-digit number)

26029569843480738227…70982079500996986399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.602 × 10⁹⁹(100-digit number)

26029569843480738227…70982079500996986401

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

5.205 × 10⁹⁹(100-digit number)

52059139686961476455…41964159001993972799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.205 × 10⁹⁹(100-digit number)

52059139686961476455…41964159001993972801

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

1.041 × 10¹⁰⁰(101-digit number)

10411827937392295291…83928318003987945599

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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