Block #533,689

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/9/2014, 9:00:06 PM · Difficulty 10.9001 · 6,275,545 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6d27c93a16c4994bbc4ef87e8433a51a455ea2bb372d0abc3990f6623e108ae9

View on Chainz ↗

Height

#533,689

Difficulty

10.900103

Transactions

Size

626 B

Version

Bits

0ae66d22

Nonce

5,231,154

Timestamp

5/9/2014, 9:00:06 PM

Confirmations

6,275,545

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

c5817062da6d3d454dfe5a6309e53c9912ed56bde20cb0900bfc8695c915fb52

Transactions (3)

Coinbased523b19098fc2e…8136cc57540851

1 in → 1 out8.4200 XPM116 B

ANSXnLY2…Sd25TjkD

d159e04a0c3791…a7abacbf81ad9d

1 in → 1 out2.9911 XPM192 B

AXCNJAvq…qsPtg17V

e880d222446682…4909d2302cf9f6

1 in → 2 out3.7951 XPM226 B

AKBkDwdh…VNdpGxTL AG8u7ddV…cU5QJSqk

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.

5.483 × 10⁹⁹(100-digit number)

54838248435844116125…66251247646431321599

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

5.483 × 10⁹⁹(100-digit number)

54838248435844116125…66251247646431321599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.483 × 10⁹⁹(100-digit number)

54838248435844116125…66251247646431321601

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

1.096 × 10¹⁰⁰(101-digit number)

10967649687168823225…32502495292862643199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.096 × 10¹⁰⁰(101-digit number)

10967649687168823225…32502495292862643201

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

2.193 × 10¹⁰⁰(101-digit number)

21935299374337646450…65004990585725286399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.193 × 10¹⁰⁰(101-digit number)

21935299374337646450…65004990585725286401

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

4.387 × 10¹⁰⁰(101-digit number)

43870598748675292900…30009981171450572799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.387 × 10¹⁰⁰(101-digit number)

43870598748675292900…30009981171450572801

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

8.774 × 10¹⁰⁰(101-digit number)

87741197497350585800…60019962342901145599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.774 × 10¹⁰⁰(101-digit number)

87741197497350585800…60019962342901145601

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

1.754 × 10¹⁰¹(102-digit number)

17548239499470117160…20039924685802291199

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 #533,689

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