Block #716,996

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/12/2014, 2:05:44 AM · Difficulty 10.9519 · 6,092,738 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

503dbcf7c1f523d8afd6c6d13c28c582233ecc85d0df78c3b15ebc6863ed1283

View on Chainz ↗

Height

#716,996

Difficulty

10.951866

Transactions

Size

424 B

Version

Bits

0af3ad82

Nonce

1,768,419,771

Timestamp

9/12/2014, 2:05:44 AM

Confirmations

6,092,738

Mined by

⛏️ P2SHAWHgwMRFWpSqEGD6HdcjRCDVcuZkevdZ8z

Merkle Root

62cef648cc7585bf8c86e6792760e2f156ae5317b423ff4e1de6eb4f0de15f39

Transactions (2)

Coinbase055d6d9c0fb145…223b4445483624

1 in → 1 out8.3300 XPM109 B

AWHgwMRF…ZkevdZ8z

ed7867302232c0…5ae1515ce4c22a

1 in → 3 out8.3100 XPM225 B

ALGAe14Z…WzpodGGa AeKNrjNj…1NEq95Ta Aa4PtTwK…H3ppZFzk

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.

8.271 × 10⁹³(94-digit number)

82716779488796718078…86877106633704983799

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

8.271 × 10⁹³(94-digit number)

82716779488796718078…86877106633704983799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.271 × 10⁹³(94-digit number)

82716779488796718078…86877106633704983801

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

1.654 × 10⁹⁴(95-digit number)

16543355897759343615…73754213267409967599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.654 × 10⁹⁴(95-digit number)

16543355897759343615…73754213267409967601

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

3.308 × 10⁹⁴(95-digit number)

33086711795518687231…47508426534819935199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.308 × 10⁹⁴(95-digit number)

33086711795518687231…47508426534819935201

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

6.617 × 10⁹⁴(95-digit number)

66173423591037374463…95016853069639870399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.617 × 10⁹⁴(95-digit number)

66173423591037374463…95016853069639870401

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

1.323 × 10⁹⁵(96-digit number)

13234684718207474892…90033706139279740799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.323 × 10⁹⁵(96-digit number)

13234684718207474892…90033706139279740801

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 #716,996

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