Block #1,692,000

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 7/28/2016, 1:29:45 AM · Difficulty 10.6845 · 5,139,786 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c1184f54ded08ec6642042349229098d85cc624289e70a8957fcd44ef30a6131

View on Chainz ↗

Height

#1,692,000

Difficulty

10.684495

Transactions

Size

1.14 KB

Version

Bits

0aaf3b15

Nonce

1,265,822,024

Timestamp

7/28/2016, 1:29:45 AM

Confirmations

5,139,786

Mined by

⛏️ P2SHAM1s8gmGpLaCY61hBiWTFgwukVhUuPfcSu

Merkle Root

f96440c15fe87e76e5d3da30048ea2b25c2f43dff36331dfce15ca0e016e5773

Transactions (2)

Coinbase3c9eebe90dcb5e…7cd6c3092aa381

1 in → 1 out8.7600 XPM109 B

AM1s8gmG…hUuPfcSu

d321b2042b77ee…2bb17abaeacb0e

6 in → 2 out71.7545 XPM967 B

AQcjeddP…AoqhXrhG ANbRAjNH…bdXLSek7

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.

4.647 × 10⁹³(94-digit number)

46471045429795598425…62534646866463736879

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

4.647 × 10⁹³(94-digit number)

46471045429795598425…62534646866463736879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.647 × 10⁹³(94-digit number)

46471045429795598425…62534646866463736881

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

9.294 × 10⁹³(94-digit number)

92942090859591196851…25069293732927473759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.294 × 10⁹³(94-digit number)

92942090859591196851…25069293732927473761

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

1.858 × 10⁹⁴(95-digit number)

18588418171918239370…50138587465854947519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.858 × 10⁹⁴(95-digit number)

18588418171918239370…50138587465854947521

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

3.717 × 10⁹⁴(95-digit number)

37176836343836478740…00277174931709895039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.717 × 10⁹⁴(95-digit number)

37176836343836478740…00277174931709895041

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

7.435 × 10⁹⁴(95-digit number)

74353672687672957481…00554349863419790079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.435 × 10⁹⁴(95-digit number)

74353672687672957481…00554349863419790081

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 #1,692,000

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