Block #735,574

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 9/22/2014, 4:14:53 PM · Difficulty 10.9755 · 6,059,569 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d95680bd7c819c8a14c4553f665387b95517236a1249c68f4a5526697e8ac70e

View on Chainz ↗

Height

#735,574

Difficulty

10.975513

Transactions

Size

1.62 KB

Version

Bits

0af9bb37

Nonce

899,676,991

Timestamp

9/22/2014, 4:14:53 PM

Confirmations

6,059,569

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

35ba0b68b928f468b43377ea839c75346fd832fd2939e6b628ed78806f5923a9

Transactions (5)

Coinbase39b4003aa35d24…afa3c32a829d02

1 in → 1 out8.3300 XPM116 B

ANSXnLY2…Sd25TjkD

192d9d36788b0a…0b03027a584bb8

3 in → 5 out3292.4637 XPM624 B

AGuisewS…kixoacNm AQUC7Hue…LL2XMoNY APep8GWy…1Au7Nepp AHPZjSeK…s4BFg7Di ANGTb4nb…F8oAXf6g

6c66eb6ea12c35…97ce7d966ebfae

1 in → 2 out7.2087 XPM226 B

AJTsLJ89…rErdMt2e AWUQc2NA…r5SMGpwU

31e018c2549417…56219600df1686

1 in → 2 out6.4595 XPM226 B

ANsZYAZy…wSk4mkms AJcpDxtA…aVDHBKRr

b1cdff5ef1a19c…768e95dc75fde7

2 in → 2 out0.5752 XPM374 B

AH5e1dQD…qqPGWERG AcZfF3gB…3zqXoCyr

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.

6.427 × 10⁹⁴(95-digit number)

64279289629512475774…05354202450978082359

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

6.427 × 10⁹⁴(95-digit number)

64279289629512475774…05354202450978082359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.427 × 10⁹⁴(95-digit number)

64279289629512475774…05354202450978082361

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

1.285 × 10⁹⁵(96-digit number)

12855857925902495154…10708404901956164719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.285 × 10⁹⁵(96-digit number)

12855857925902495154…10708404901956164721

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

2.571 × 10⁹⁵(96-digit number)

25711715851804990309…21416809803912329439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.571 × 10⁹⁵(96-digit number)

25711715851804990309…21416809803912329441

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

5.142 × 10⁹⁵(96-digit number)

51423431703609980619…42833619607824658879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.142 × 10⁹⁵(96-digit number)

51423431703609980619…42833619607824658881

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

1.028 × 10⁹⁶(97-digit number)

10284686340721996123…85667239215649317759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.028 × 10⁹⁶(97-digit number)

10284686340721996123…85667239215649317761

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

2.056 × 10⁹⁶(97-digit number)

20569372681443992247…71334478431298635519

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