Block #1,534,760

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/10/2016, 11:07:50 AM · Difficulty 10.6183 · 5,281,532 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ba87627e2383d46c0429c9086344b06b0e8d32be0b38fc650598361695db7ec9

View on Chainz ↗

Height

#1,534,760

Difficulty

10.618314

Transactions

Size

22.43 KB

Version

Bits

0a9e49cc

Nonce

1,685,355,035

Timestamp

4/10/2016, 11:07:50 AM

Confirmations

5,281,532

Mined by

⛏️ P2SHAPBrCcmq15kPnXxybAyFQkLTDi5SSfLPJn

Merkle Root

fc54bdd038be0fa6dfa9ccf4a494f0d128ae833c5a06c503325c1a18588b82b6

Transactions (4)

Coinbase49fc201c4c4b3c…ca34eb681e2d5d

1 in → 1 out9.1000 XPM110 B

APBrCcmq…5SSfLPJn

7eed248e9376e4…4d53e9f0db8f8b

51 in → 1 out377.7405 XPM7.42 KB

ATv3nf4U…zFrknQMg

c2f683afad58c4…730723585790cf

51 in → 1 out148.4515 XPM7.40 KB

AWQ6EbgN…16GUyMxg

85cb5c3a0c608b…1566638d57a8a6

51 in → 1 out242.8899 XPM7.41 KB

AKwAZQ5a…zh84Q1k2

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.

3.973 × 10⁹³(94-digit number)

39738055428305124607…64386557828448687789

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

3.973 × 10⁹³(94-digit number)

39738055428305124607…64386557828448687789

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.973 × 10⁹³(94-digit number)

39738055428305124607…64386557828448687791

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

7.947 × 10⁹³(94-digit number)

79476110856610249215…28773115656897375579

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.947 × 10⁹³(94-digit number)

79476110856610249215…28773115656897375581

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

1.589 × 10⁹⁴(95-digit number)

15895222171322049843…57546231313794751159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.589 × 10⁹⁴(95-digit number)

15895222171322049843…57546231313794751161

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

3.179 × 10⁹⁴(95-digit number)

31790444342644099686…15092462627589502319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.179 × 10⁹⁴(95-digit number)

31790444342644099686…15092462627589502321

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

6.358 × 10⁹⁴(95-digit number)

63580888685288199372…30184925255179004639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.358 × 10⁹⁴(95-digit number)

63580888685288199372…30184925255179004641

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 #1,534,760

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