Block #1,679,420

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 7/19/2016, 3:20:32 AM · Difficulty 10.7002 · 5,151,127 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4dedd4b74d5cbab3bf84c4bdb5269cab4ab842fc86f9e0bcbc7ca21e3a74b081

View on Chainz ↗

Height

#1,679,420

Difficulty

10.700159

Transactions

Size

1015 B

Version

Bits

0ab33d98

Nonce

513,760,024

Timestamp

7/19/2016, 3:20:32 AM

Confirmations

5,151,127

Mined by

⛏️ P2SHAQ9bZyiWAPhMTZyCXejtjL95LCSUusxQuN

Merkle Root

7a141cdf3a428029d1f92853a062625b8a47c8fa6b57dad4b444e2717406fdce

Transactions (2)

Coinbasec1c338e573ad3a…54dd6c504fa360

1 in → 1 out8.7300 XPM109 B

AQ9bZyiW…SUusxQuN

47c5fe1eea39d5…8b99b287184091

5 in → 2 out167.7480 XPM816 B

AQcjeddP…AoqhXrhG AR11CNL7…1huokKuJ

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.

2.699 × 10⁹³(94-digit number)

26993897221772241157…30558563169880820599

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

2.699 × 10⁹³(94-digit number)

26993897221772241157…30558563169880820599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.699 × 10⁹³(94-digit number)

26993897221772241157…30558563169880820601

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

5.398 × 10⁹³(94-digit number)

53987794443544482315…61117126339761641199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.398 × 10⁹³(94-digit number)

53987794443544482315…61117126339761641201

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

1.079 × 10⁹⁴(95-digit number)

10797558888708896463…22234252679523282399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.079 × 10⁹⁴(95-digit number)

10797558888708896463…22234252679523282401

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

2.159 × 10⁹⁴(95-digit number)

21595117777417792926…44468505359046564799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.159 × 10⁹⁴(95-digit number)

21595117777417792926…44468505359046564801

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

4.319 × 10⁹⁴(95-digit number)

43190235554835585852…88937010718093129599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.319 × 10⁹⁴(95-digit number)

43190235554835585852…88937010718093129601

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 #1,679,420

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