Block #2,257,797

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 8/18/2017, 8:58:04 PM · Difficulty 10.9521 · 4,581,875 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

29c5ee812478a609b95bd754bd604e8867f77d435a3d3ca73364bae8dd5c807b

View on Chainz ↗

Height

#2,257,797

Difficulty

10.952072

Transactions

Size

2.78 KB

Version

Bits

0af3bb00

Nonce

1,186,028,655

Timestamp

8/18/2017, 8:58:04 PM

Confirmations

4,581,875

Mined by

⛏️ P2SHAahm4nYwqEngEH4zhRrNHiPS5fra6yQV1s

Merkle Root

3c5485fd86851ea7ca6b82ba1f4692bbd1a3baba632ad87839cbb9dfa00c9edf

Transactions (4)

Coinbase592860b809ad87…362e0b2b2fd5d3

1 in → 1 out8.3600 XPM110 B

Aahm4nYw…ra6yQV1s

1d7206bddbee27…6d02071a2a03e8

15 in → 2 out120.1584 XPM1.78 KB

ALT4uckg…8i3K6WZU ATh8YQMK…JTRwegQa

d1db5d31fa7ee7…bdc669b44fa047

2 in → 2 out13.5919 XPM341 B

AWddcU83…RSBKXbX6 AU7AZJNb…pnzFDqqu

519291e0a1d90d…29a8dfc51b2920

3 in → 2 out10.2409 XPM487 B

AbKTiZFs…jnXNkDw6 AQEfWikv…AFFvFEyz

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.

2.230 × 10⁹⁴(95-digit number)

22306060354686383588…18250473782719708159

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

2.230 × 10⁹⁴(95-digit number)

22306060354686383588…18250473782719708159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.230 × 10⁹⁴(95-digit number)

22306060354686383588…18250473782719708161

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

4.461 × 10⁹⁴(95-digit number)

44612120709372767176…36500947565439416319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.461 × 10⁹⁴(95-digit number)

44612120709372767176…36500947565439416321

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

8.922 × 10⁹⁴(95-digit number)

89224241418745534353…73001895130878832639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.922 × 10⁹⁴(95-digit number)

89224241418745534353…73001895130878832641

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

1.784 × 10⁹⁵(96-digit number)

17844848283749106870…46003790261757665279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.784 × 10⁹⁵(96-digit number)

17844848283749106870…46003790261757665281

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

3.568 × 10⁹⁵(96-digit number)

35689696567498213741…92007580523515330559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.568 × 10⁹⁵(96-digit number)

35689696567498213741…92007580523515330561

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 #2,257,797

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