Block #726,975

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/18/2014, 6:47:44 AM · Difficulty 10.9612 · 6,076,705 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

193f379cbd286227d8b729ab8b4ed83d9f07fcbfe1ce1dcc240f973bcc2f92c9

View on Chainz ↗

Height

#726,975

Difficulty

10.961236

Transactions

Size

1.15 KB

Version

Bits

0af6138a

Nonce

228,593,217

Timestamp

9/18/2014, 6:47:44 AM

Confirmations

6,076,705

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

497cb55cd70e8a9a6860f720973d1db8c4e6907002875114d13a5a0c9550cae9

Transactions (4)

Coinbase56e0c14a4762ee…e5a20c967c8bf0

1 in → 1 out8.3400 XPM116 B

ANSXnLY2…Sd25TjkD

b9fe0fa22167f2…35ca30be6d1924

3 in → 2 out10.2650 XPM521 B

ARx2sCJ6…1ApfHVnB ALmFD8hY…hZD4B2pa

cba74f06c747e4…5f53453cc68316

1 in → 2 out8.3000 XPM226 B

ANZUxYNW…P1pZfYxg AG1Vksq6…trSxcKeU

e9dc9c02f773ef…4800f0356d776b

1 in → 2 out8.3000 XPM225 B

AHqZtsfn…WrCGjM3J AM7eEzqg…hqeW9YqA

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.

1.573 × 10⁹⁷(98-digit number)

15738470960581540198…69677193754595302399

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

1.573 × 10⁹⁷(98-digit number)

15738470960581540198…69677193754595302399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.573 × 10⁹⁷(98-digit number)

15738470960581540198…69677193754595302401

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

3.147 × 10⁹⁷(98-digit number)

31476941921163080396…39354387509190604799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.147 × 10⁹⁷(98-digit number)

31476941921163080396…39354387509190604801

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

6.295 × 10⁹⁷(98-digit number)

62953883842326160793…78708775018381209599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.295 × 10⁹⁷(98-digit number)

62953883842326160793…78708775018381209601

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

1.259 × 10⁹⁸(99-digit number)

12590776768465232158…57417550036762419199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.259 × 10⁹⁸(99-digit number)

12590776768465232158…57417550036762419201

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

2.518 × 10⁹⁸(99-digit number)

25181553536930464317…14835100073524838399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.518 × 10⁹⁸(99-digit number)

25181553536930464317…14835100073524838401

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