Block #735,032

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 9/22/2014, 9:05:48 AM · Difficulty 10.9749 · 6,091,389 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6fe2c86baaf2383a9a65e4c533e66ac9bc639b58a0e91a7b6c65c15e4d1cb92a

View on Chainz ↗

Height

#735,032

Difficulty

10.974940

Transactions

Size

1.51 KB

Version

Bits

0af995ab

Nonce

107,696,920

Timestamp

9/22/2014, 9:05:48 AM

Confirmations

6,091,389

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

3049c22150e25b889c326d14ff3ed4e99dcba662f3c027774908926453a6e82f

Transactions (4)

Coinbase1b9fc3fd19f947…5754a2260f43ab

1 in → 1 out8.3200 XPM116 B

ANSXnLY2…Sd25TjkD

f73ea009dfe231…30a336d9592376

4 in → 2 out20.9418 XPM668 B

AJwLt2hK…sVKQPZtR AKhyrrXd…9fDt15dr

a2a16e83cc1249…c7254ad5eeb200

1 in → 5 out8.2900 XPM295 B

Abz9CAqQ…etH6XVc6 AH1wEe2R…srAfPtHd AeKNrjNj…1NEq95Ta AJcmFad4…YNAMFS3w AYk6SdQf…UGcYbb4t

6f9b20177520c1…11962be54a016f

2 in → 2 out11.3577 XPM373 B

Adsdktbi…qQMZ5eiC AKFMpVJb…yxf16bgZ

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.

1.268 × 10⁹⁷(98-digit number)

12685618028863983806…71486322823345968639

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

1.268 × 10⁹⁷(98-digit number)

12685618028863983806…71486322823345968639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.268 × 10⁹⁷(98-digit number)

12685618028863983806…71486322823345968641

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

2.537 × 10⁹⁷(98-digit number)

25371236057727967613…42972645646691937279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.537 × 10⁹⁷(98-digit number)

25371236057727967613…42972645646691937281

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

5.074 × 10⁹⁷(98-digit number)

50742472115455935226…85945291293383874559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.074 × 10⁹⁷(98-digit number)

50742472115455935226…85945291293383874561

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

1.014 × 10⁹⁸(99-digit number)

10148494423091187045…71890582586767749119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.014 × 10⁹⁸(99-digit number)

10148494423091187045…71890582586767749121

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

2.029 × 10⁹⁸(99-digit number)

20296988846182374090…43781165173535498239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.029 × 10⁹⁸(99-digit number)

20296988846182374090…43781165173535498241

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

4.059 × 10⁹⁸(99-digit number)

40593977692364748181…87562330347070996479

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #735,032

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