Block #536,809

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/11/2014, 1:55:36 PM · Difficulty 10.9126 · 6,259,361 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c65eaa8e0fa8fdc1a072a9660155bf42775b5158c221bb1c6d59fe80bdf0db86

View on Chainz ↗

Height

#536,809

Difficulty

10.912585

Transactions

Size

661 B

Version

Bits

0ae99f2d

Nonce

15,167,533

Timestamp

5/11/2014, 1:55:36 PM

Confirmations

6,259,361

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

2ae0cd3ec79fd71188c7fd0c70ae5aaff1ca05c53ae49f74035b73d05bd4f65c

Transactions (3)

Coinbase729726b508fe56…19d2e5039e295c

1 in → 1 out8.4000 XPM116 B

ANSXnLY2…Sd25TjkD

fb8f76ae69376e…f717be1309f9fb

1 in → 3 out8.3900 XPM226 B

AGRJf5c9…j28JnLsV AeKNrjNj…1NEq95Ta AcNovFbg…sJ1oLH5E

bd9873251d516c…2eee2f9ef0816b

1 in → 2 out2.2371 XPM226 B

AYRCBwWC…eyS2mHDw AGdWVjRk…LFVsqCnK

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.

3.263 × 10¹⁰²(103-digit number)

32631925765524903194…28848584738281881599

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

3.263 × 10¹⁰²(103-digit number)

32631925765524903194…28848584738281881599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.263 × 10¹⁰²(103-digit number)

32631925765524903194…28848584738281881601

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

6.526 × 10¹⁰²(103-digit number)

65263851531049806388…57697169476563763199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.526 × 10¹⁰²(103-digit number)

65263851531049806388…57697169476563763201

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

1.305 × 10¹⁰³(104-digit number)

13052770306209961277…15394338953127526399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.305 × 10¹⁰³(104-digit number)

13052770306209961277…15394338953127526401

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

2.610 × 10¹⁰³(104-digit number)

26105540612419922555…30788677906255052799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.610 × 10¹⁰³(104-digit number)

26105540612419922555…30788677906255052801

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

5.221 × 10¹⁰³(104-digit number)

52211081224839845111…61577355812510105599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.221 × 10¹⁰³(104-digit number)

52211081224839845111…61577355812510105601

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

1.044 × 10¹⁰⁴(105-digit number)

10442216244967969022…23154711625020211199

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