Block #535,689

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/11/2014, 1:57:06 AM · Difficulty 10.9053 · 6,291,186 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

81ef6d764e9dfefd610be4f534eb9af5e873c5b6c1721a1eca4ebbbab8b593ec

View on Chainz ↗

Height

#535,689

Difficulty

10.905279

Transactions

Size

958 B

Version

Bits

0ae7c05d

Nonce

357,266,708

Timestamp

5/11/2014, 1:57:06 AM

Confirmations

6,291,186

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

3f9440b434ed10f8fd43b1a360bc49aa83b165664672dcf220bfcfe25ca0fa30

Transactions (3)

Coinbasead1552a64c4d7d…583d38833fcdf1

1 in → 1 out8.4200 XPM116 B

ANSXnLY2…Sd25TjkD

12ebe30a21d64a…a8d7d2320730a3

3 in → 2 out7.6809 XPM523 B

AXnXEwg6…un9Teu49 AXhZg1po…6mF2w9PB

1bf2ccf893f216…5b80e763e9ca95

1 in → 2 out5.3163 XPM227 B

AM8F4Due…U53uua4k APhsb7GR…rrAgcC5c

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.

8.658 × 10⁹⁸(99-digit number)

86589480427574667939…65646667581342153759

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

8.658 × 10⁹⁸(99-digit number)

86589480427574667939…65646667581342153759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.658 × 10⁹⁸(99-digit number)

86589480427574667939…65646667581342153761

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

1.731 × 10⁹⁹(100-digit number)

17317896085514933587…31293335162684307519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.731 × 10⁹⁹(100-digit number)

17317896085514933587…31293335162684307521

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

3.463 × 10⁹⁹(100-digit number)

34635792171029867175…62586670325368615039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.463 × 10⁹⁹(100-digit number)

34635792171029867175…62586670325368615041

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

6.927 × 10⁹⁹(100-digit number)

69271584342059734351…25173340650737230079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.927 × 10⁹⁹(100-digit number)

69271584342059734351…25173340650737230081

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

1.385 × 10¹⁰⁰(101-digit number)

13854316868411946870…50346681301474460159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.385 × 10¹⁰⁰(101-digit number)

13854316868411946870…50346681301474460161

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

2.770 × 10¹⁰⁰(101-digit number)

27708633736823893740…00693362602948920319

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 #535,689

Cookie Preferences