Block #1,593,711

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/21/2016, 7:15:25 AM · Difficulty 10.6317 · 5,222,983 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9c8153134c3f64f2f4211d5af5e7f9f4ce87a975f6f5c1827a06338f6572f781

View on Chainz ↗

Height

#1,593,711

Difficulty

10.631675

Transactions

Size

19.93 KB

Version

Bits

0aa1b577

Nonce

56,251,869

Timestamp

5/21/2016, 7:15:25 AM

Confirmations

5,222,983

Mined by

⛏️ P2SHAWw55rzsbt6XSKV1gb8JUbqLBgcrnyqv1T

Merkle Root

bcbf3c7c9adfdf4f2b0de674aee31f301574ca79275c720de8f864da87e1a86b

Transactions (2)

Coinbasef0943bf1e9a4f9…7f2b3b89e35e81

1 in → 1 out9.3500 XPM110 B

AWw55rzs…crnyqv1T

2b5e105659defe…296179f50c0b6b

136 in → 2 out4826.3616 XPM19.73 KB

AGXTevcc…MC6hJxDi AQHE5e6H…xDwU3vYU

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.

7.233 × 10⁹⁴(95-digit number)

72338281207065018497…52508844565480451839

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

7.233 × 10⁹⁴(95-digit number)

72338281207065018497…52508844565480451839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.233 × 10⁹⁴(95-digit number)

72338281207065018497…52508844565480451841

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

1.446 × 10⁹⁵(96-digit number)

14467656241413003699…05017689130960903679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.446 × 10⁹⁵(96-digit number)

14467656241413003699…05017689130960903681

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

2.893 × 10⁹⁵(96-digit number)

28935312482826007399…10035378261921807359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.893 × 10⁹⁵(96-digit number)

28935312482826007399…10035378261921807361

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

5.787 × 10⁹⁵(96-digit number)

57870624965652014798…20070756523843614719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.787 × 10⁹⁵(96-digit number)

57870624965652014798…20070756523843614721

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

1.157 × 10⁹⁶(97-digit number)

11574124993130402959…40141513047687229439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.157 × 10⁹⁶(97-digit number)

11574124993130402959…40141513047687229441

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 #1,593,711

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