Block #189,904

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/2/2013, 3:13:40 AM · Difficulty 9.8737 · 6,624,311 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

00488c1a288e66374bebd1bc768095ea9c51cac653fc9d4b7ec0119c290bf1ff

View on Chainz ↗

Height

#189,904

Difficulty

9.873736

Transactions

Size

1.08 KB

Version

Bits

09dfad2f

Nonce

10,103

Timestamp

10/2/2013, 3:13:40 AM

Confirmations

6,624,311

Mined by

⛏️ P2SHANhBYN2SEW7rbkjcwTxrVMFUB1W53F3KTQ

Merkle Root

f6581d51aa7bcc33cc2d85790da54536440d8e0a9af5a0c05262be7d9b04d6c0

Transactions (5)

Coinbase6345509f04bc11…ebc11464343afc

1 in → 1 out10.2800 XPM109 B

ANhBYN2S…W53F3KTQ

66360186f4f0ba…ae667c4c95b8e5

1 in → 2 out1.9900 XPM226 B

AS2M5ijA…CNnnZzMB AZNbKtqd…rcimD3Fa

e7c18176a96299…7bc3a31d773b2b

1 in → 2 out91.8292 XPM227 B

Ab5uypEx…mVqX8FmY AY4AtqdV…TUXSUndj

6d24b8eb21b28b…76ccb99345e7a2

1 in → 2 out1.1700 XPM226 B

APDPqsrE…7i3RvFVS AWT8GCtb…pdh2u5FB

8193a65c88e4b8…03aead722d2095

1 in → 2 out8.0963 XPM226 B

AdjgM36g…QSZWQb5w AXZvTo9z…YBDPsrv2

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.

1.343 × 10⁹²(93-digit number)

13436770844105740126…76531161588178568719

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

1.343 × 10⁹²(93-digit number)

13436770844105740126…76531161588178568719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.343 × 10⁹²(93-digit number)

13436770844105740126…76531161588178568721

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

2.687 × 10⁹²(93-digit number)

26873541688211480252…53062323176357137439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.687 × 10⁹²(93-digit number)

26873541688211480252…53062323176357137441

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

5.374 × 10⁹²(93-digit number)

53747083376422960505…06124646352714274879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.374 × 10⁹²(93-digit number)

53747083376422960505…06124646352714274881

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

1.074 × 10⁹³(94-digit number)

10749416675284592101…12249292705428549759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.074 × 10⁹³(94-digit number)

10749416675284592101…12249292705428549761

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

2.149 × 10⁹³(94-digit number)

21498833350569184202…24498585410857099519

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 #189,904

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