Block #1,692,745

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 7/28/2016, 2:46:14 PM · Difficulty 10.6811 · 5,137,856 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

081529dc3808bd213eb3e135f2c94b319710d5b21e29bf33a872d2835a187878

View on Chainz ↗

Height

#1,692,745

Difficulty

10.681085

Transactions

Size

1019 B

Version

Bits

0aae5b97

Nonce

316,209,797

Timestamp

7/28/2016, 2:46:14 PM

Confirmations

5,137,856

Mined by

⛏️ P2SHAagg7sRwk8zh2Eb7XsgMQ6YVWja7nS9wWK

Merkle Root

2aed8cafd2a5db4c6f2bc4ba890526949b6c11df6677f4cf9ed7a0dfb6a10c42

Transactions (2)

Coinbase0d6ec17ff92201…a7de0a89926233

1 in → 1 out8.7600 XPM110 B

Aagg7sRw…a7nS9wWK

21f3558ffbb771…9eb1b0e5bf1afb

5 in → 2 out53.9654 XPM820 B

AYoi7Hj9…tsi8RkLg AQcjeddP…AoqhXrhG

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.

8.998 × 10⁹²(93-digit number)

89984525706111661657…89468964754293273599

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

8.998 × 10⁹²(93-digit number)

89984525706111661657…89468964754293273599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.998 × 10⁹²(93-digit number)

89984525706111661657…89468964754293273601

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

1.799 × 10⁹³(94-digit number)

17996905141222332331…78937929508586547199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.799 × 10⁹³(94-digit number)

17996905141222332331…78937929508586547201

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

3.599 × 10⁹³(94-digit number)

35993810282444664663…57875859017173094399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.599 × 10⁹³(94-digit number)

35993810282444664663…57875859017173094401

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

7.198 × 10⁹³(94-digit number)

71987620564889329326…15751718034346188799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.198 × 10⁹³(94-digit number)

71987620564889329326…15751718034346188801

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

1.439 × 10⁹⁴(95-digit number)

14397524112977865865…31503436068692377599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.439 × 10⁹⁴(95-digit number)

14397524112977865865…31503436068692377601

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 #1,692,745

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