Block #2,269,673

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 8/27/2017, 2:41:46 AM · Difficulty 10.9525 · 4,556,512 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

70bc1ca52438592874f65435d73568b7500411b08cd84345778143bd1bd4e5a6

View on Chainz ↗

Height

#2,269,673

Difficulty

10.952531

Transactions

Size

1.79 KB

Version

Bits

0af3d90b

Nonce

1,199,958,965

Timestamp

8/27/2017, 2:41:46 AM

Confirmations

4,556,512

Mined by

⛏️ P2SHATS5uJSkBNZuf4XcaQLnqweN66W4C8f29A

Merkle Root

5c64f54a8cac738dd1fed3c17e228044147436bfa6dbbfcb4a8c7eacac997bbd

Transactions (3)

Coinbaseb473e509aa9bbf…155ad12eee6892

1 in → 1 out8.3500 XPM109 B

ATS5uJSk…W4C8f29A

5f8c18f97db6b5…e51d6b37fdea48

9 in → 2 out393.3592 XPM1.38 KB

Aa4LtY7N…qEvWhnnQ AWVBJzri…1sMkuo1y

e4ce32e001b21c…0670bfd6999147

1 in → 2 out20979.2157 XPM226 B

AWR1RjHt…Sq4hsmPS AGFVfREX…cgCHb18K

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.

1.418 × 10⁹⁴(95-digit number)

14188225052813820825…33084369927033994879

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

1.418 × 10⁹⁴(95-digit number)

14188225052813820825…33084369927033994879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.418 × 10⁹⁴(95-digit number)

14188225052813820825…33084369927033994881

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

2.837 × 10⁹⁴(95-digit number)

28376450105627641650…66168739854067989759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.837 × 10⁹⁴(95-digit number)

28376450105627641650…66168739854067989761

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

5.675 × 10⁹⁴(95-digit number)

56752900211255283300…32337479708135979519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.675 × 10⁹⁴(95-digit number)

56752900211255283300…32337479708135979521

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

1.135 × 10⁹⁵(96-digit number)

11350580042251056660…64674959416271959039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.135 × 10⁹⁵(96-digit number)

11350580042251056660…64674959416271959041

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

2.270 × 10⁹⁵(96-digit number)

22701160084502113320…29349918832543918079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.270 × 10⁹⁵(96-digit number)

22701160084502113320…29349918832543918081

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 #2,269,673

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