Block #1,065,518

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/18/2015, 11:40:02 PM · Difficulty 10.7333 · 5,741,137 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5f2023dbc58dc98381c224f84ba7df5a957792c6169e619a8708293601f79822

View on Chainz ↗

Height

#1,065,518

Difficulty

10.733310

Transactions

Size

432 B

Version

Bits

0abbba31

Nonce

42,294,301

Timestamp

5/18/2015, 11:40:02 PM

Confirmations

5,741,137

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

097de9d06e246d46669cd019c1e8b6f11907082048fcf4ad61cf4658e8f4884a

Transactions (2)

Coinbase170085beb7ef7e…beff28fa65c6e9

1 in → 1 out8.6800 XPM116 B

ANSXnLY2…Sd25TjkD

6d28b5e8fae7e5…a741f5ee756cdb

1 in → 2 out1.5707 XPM225 B

AKSqnEcm…Ao4JMqi1 AHmcchxr…vBbydp5n

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.

3.906 × 10⁹⁶(97-digit number)

39061873390845798715…84299359845921935999

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

3.906 × 10⁹⁶(97-digit number)

39061873390845798715…84299359845921935999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.906 × 10⁹⁶(97-digit number)

39061873390845798715…84299359845921936001

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

7.812 × 10⁹⁶(97-digit number)

78123746781691597431…68598719691843871999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.812 × 10⁹⁶(97-digit number)

78123746781691597431…68598719691843872001

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

1.562 × 10⁹⁷(98-digit number)

15624749356338319486…37197439383687743999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.562 × 10⁹⁷(98-digit number)

15624749356338319486…37197439383687744001

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

3.124 × 10⁹⁷(98-digit number)

31249498712676638972…74394878767375487999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.124 × 10⁹⁷(98-digit number)

31249498712676638972…74394878767375488001

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

6.249 × 10⁹⁷(98-digit number)

62498997425353277944…48789757534750975999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.249 × 10⁹⁷(98-digit number)

62498997425353277944…48789757534750976001

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 #1,065,518

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