Block #1,534,516

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/10/2016, 7:20:23 AM · Difficulty 10.6170 · 5,292,713 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7e29451914f9c40192eb212c5e9ca2cc4f92b121c72994553a6e2607d89fd3ad

View on Chainz ↗

Height

#1,534,516

Difficulty

10.616970

Transactions

Size

7.61 KB

Version

Bits

0a9df1b7

Nonce

609,454,045

Timestamp

4/10/2016, 7:20:23 AM

Confirmations

5,292,713

Mined by

⛏️ P2SHAWmeDsX8k9ChP7yWtqxwbtquaXvUYkPk13

Merkle Root

146c4fd311114f16d2e6b5bcc95c85d1e1220184d2581665107988b2c418a729

Transactions (2)

Coinbasead994b851bbda0…ff64089f1efdea

1 in → 1 out8.9400 XPM110 B

AWmeDsX8…vUYkPk13

4a47cd5deb8bfc…a79dad5d5af180

51 in → 1 out575.4099 XPM7.41 KB

AcfLdneB…VmqDWSh7

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.

6.026 × 10⁹⁵(96-digit number)

60266598507583225433…20027323100189222399

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

6.026 × 10⁹⁵(96-digit number)

60266598507583225433…20027323100189222399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.026 × 10⁹⁵(96-digit number)

60266598507583225433…20027323100189222401

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

1.205 × 10⁹⁶(97-digit number)

12053319701516645086…40054646200378444799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.205 × 10⁹⁶(97-digit number)

12053319701516645086…40054646200378444801

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

2.410 × 10⁹⁶(97-digit number)

24106639403033290173…80109292400756889599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.410 × 10⁹⁶(97-digit number)

24106639403033290173…80109292400756889601

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

4.821 × 10⁹⁶(97-digit number)

48213278806066580347…60218584801513779199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.821 × 10⁹⁶(97-digit number)

48213278806066580347…60218584801513779201

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

9.642 × 10⁹⁶(97-digit number)

96426557612133160694…20437169603027558399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.642 × 10⁹⁶(97-digit number)

96426557612133160694…20437169603027558401

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 #1,534,516

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