Block #1,310,723

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/3/2015, 12:16:31 PM · Difficulty 10.8485 · 5,507,018 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

360627523d984ba0c9765a73f44c68e6b46e03d61735e0e89752aa2ecd627fed

View on Chainz ↗

Height

#1,310,723

Difficulty

10.848532

Transactions

Size

22.67 KB

Version

Bits

0ad93967

Nonce

265,515,437

Timestamp

11/3/2015, 12:16:31 PM

Confirmations

5,507,018

Mined by

⛏️ P2SHANj5SygWmfMGsccqCqEo8DhdUQHHBCTziJ

Merkle Root

97a707f2f49ef8e1e5490a3ec9792d8ddeb501c9e69da887ddd536ebfb3bca0e

Transactions (2)

Coinbasef57924baf03e80…ff5b3a97ea7318

1 in → 1 out8.7600 XPM110 B

ANj5SygW…HHBCTziJ

1a6997facc583d…c84e8eb4f79fcc

155 in → 2 out463.4390 XPM22.48 KB

AeNYqawm…GzYnccKL AdwSuNCM…mtf8NZck

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.

5.866 × 10⁹³(94-digit number)

58667275563877154965…79194501447529497479

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

5.866 × 10⁹³(94-digit number)

58667275563877154965…79194501447529497479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.866 × 10⁹³(94-digit number)

58667275563877154965…79194501447529497481

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

1.173 × 10⁹⁴(95-digit number)

11733455112775430993…58389002895058994959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.173 × 10⁹⁴(95-digit number)

11733455112775430993…58389002895058994961

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

2.346 × 10⁹⁴(95-digit number)

23466910225550861986…16778005790117989919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.346 × 10⁹⁴(95-digit number)

23466910225550861986…16778005790117989921

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

4.693 × 10⁹⁴(95-digit number)

46933820451101723972…33556011580235979839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.693 × 10⁹⁴(95-digit number)

46933820451101723972…33556011580235979841

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

9.386 × 10⁹⁴(95-digit number)

93867640902203447944…67112023160471959679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.386 × 10⁹⁴(95-digit number)

93867640902203447944…67112023160471959681

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 #1,310,723

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