Block #562,164

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/25/2014, 10:54:14 PM · Difficulty 10.9659 · 6,248,454 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

99c1b5abe0c07670786d3ba45454018fe008e4817d819025c99d63a36086c702

View on Chainz ↗

Height

#562,164

Difficulty

10.965930

Transactions

Size

885 B

Version

Bits

0af7472d

Nonce

103,332,324

Timestamp

5/25/2014, 10:54:14 PM

Confirmations

6,248,454

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

56c981eb4f3ef63cf807396bec32b855e7b892270d7e699d18dc97ea82c44830

Transactions (4)

Coinbase80b878482e1530…df835860f1dc3f

1 in → 1 out8.3300 XPM116 B

ANSXnLY2…Sd25TjkD

b786839fe6613a…c9a64d1daec692

1 in → 2 out4.4107 XPM225 B

APrRio7K…HeLcD2UT APdCykJd…xXiKaNwY

e538ab889f76e3…7982dd28c5aad2

1 in → 2 out3.4154 XPM226 B

ALNQaD7f…2g74yYvV AajEDQ7A…SbvKQXKY

e3d2513fe546a2…bacb1c224a83b0

1 in → 2 out1.1635 XPM226 B

AdffMvcM…gik74NXY AS9ZCvju…bu3NEFwZ

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.

2.134 × 10⁹⁹(100-digit number)

21344768228903638711…72755317688263925759

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

2.134 × 10⁹⁹(100-digit number)

21344768228903638711…72755317688263925759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.134 × 10⁹⁹(100-digit number)

21344768228903638711…72755317688263925761

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

4.268 × 10⁹⁹(100-digit number)

42689536457807277423…45510635376527851519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.268 × 10⁹⁹(100-digit number)

42689536457807277423…45510635376527851521

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

8.537 × 10⁹⁹(100-digit number)

85379072915614554847…91021270753055703039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.537 × 10⁹⁹(100-digit number)

85379072915614554847…91021270753055703041

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

1.707 × 10¹⁰⁰(101-digit number)

17075814583122910969…82042541506111406079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.707 × 10¹⁰⁰(101-digit number)

17075814583122910969…82042541506111406081

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

3.415 × 10¹⁰⁰(101-digit number)

34151629166245821938…64085083012222812159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.415 × 10¹⁰⁰(101-digit number)

34151629166245821938…64085083012222812161

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

6.830 × 10¹⁰⁰(101-digit number)

68303258332491643877…28170166024445624319

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 #562,164

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