Block #162,623

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/13/2013, 10:48:44 AM · Difficulty 9.8613 · 6,645,406 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

53b36ed7ed8c0c0b4ece2976a7af1005a09f52bab4c24345f9ee44198107ff42

View on Chainz ↗

Height

#162,623

Difficulty

9.861310

Transactions

Size

1007 B

Version

Bits

09dc7ed5

Nonce

156,496

Timestamp

9/13/2013, 10:48:44 AM

Confirmations

6,645,406

Mined by

⛏️ P2SHANkSBqbEXP5SFNG3bGPJ6iV1UsLajBMwP7

Merkle Root

ae2cccc879c1ede199fd3ea1793bb8914e7c7e93af88c748818af9f7e595c1d1

Transactions (4)

Coinbasea3c63829951435…c85c50f2af60ca

1 in → 1 out10.3000 XPM109 B

ANkSBqbE…LajBMwP7

a58eee2e12165a…06965df23fbf86

1 in → 1 out10.2400 XPM158 B

AYKVeNA9…BbJrTDhi

7647d04e89f3b5…e7ad690c2527b0

1 in → 1 out10.2700 XPM159 B

AXN43cfu…VpGesSCW

b274292b08aa2e…468254cdd8f1b4

3 in → 2 out11.1300 XPM488 B

AZiZ3BSK…ouABkYiL AYLXNNVT…Vby4Ncy6

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.

2.958 × 10¹⁰¹(102-digit number)

29589887803629382780…92254504978033591749

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

2.958 × 10¹⁰¹(102-digit number)

29589887803629382780…92254504978033591749

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.958 × 10¹⁰¹(102-digit number)

29589887803629382780…92254504978033591751

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

5.917 × 10¹⁰¹(102-digit number)

59179775607258765561…84509009956067183499

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.917 × 10¹⁰¹(102-digit number)

59179775607258765561…84509009956067183501

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

1.183 × 10¹⁰²(103-digit number)

11835955121451753112…69018019912134366999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.183 × 10¹⁰²(103-digit number)

11835955121451753112…69018019912134367001

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

2.367 × 10¹⁰²(103-digit number)

23671910242903506224…38036039824268733999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.367 × 10¹⁰²(103-digit number)

23671910242903506224…38036039824268734001

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

4.734 × 10¹⁰²(103-digit number)

47343820485807012449…76072079648537467999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.734 × 10¹⁰²(103-digit number)

47343820485807012449…76072079648537468001

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 #162,623

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