Block #528,187

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/6/2014, 12:14:03 PM · Difficulty 10.8860 · 6,270,605 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

85a0ca146f596da20908173c0c6697b6f7eea245c9909c1492072c7357b35a43

View on Chainz ↗

Height

#528,187

Difficulty

10.886017

Transactions

Size

658 B

Version

Bits

0ae2d207

Nonce

127,646,149

Timestamp

5/6/2014, 12:14:03 PM

Confirmations

6,270,605

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

0bec5b4e98a9b71634b5ed5db2160ce0f85fe328b3fa4613cf89568700d9b72f

Transactions (3)

Coinbaseebcb911f9f8f38…145f118a5f2d9a

1 in → 1 out8.4400 XPM116 B

ANSXnLY2…Sd25TjkD

4fea74d3f0fa52…6efc9d60aad780

1 in → 2 out146.4782 XPM226 B

AJkPiJUb…6B9osKNR AM8GuxnN…AfjbhWoV

60716befb80357…37f1cba4477ff7

1 in → 2 out122.6591 XPM225 B

AXLbkdEt…XRvVct5T AHzLyubg…mPhgdoLo

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.

1.534 × 10⁹⁸(99-digit number)

15346823913850402250…76767218006253248749

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

1.534 × 10⁹⁸(99-digit number)

15346823913850402250…76767218006253248749

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.534 × 10⁹⁸(99-digit number)

15346823913850402250…76767218006253248751

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

3.069 × 10⁹⁸(99-digit number)

30693647827700804500…53534436012506497499

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.069 × 10⁹⁸(99-digit number)

30693647827700804500…53534436012506497501

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

6.138 × 10⁹⁸(99-digit number)

61387295655401609000…07068872025012994999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.138 × 10⁹⁸(99-digit number)

61387295655401609000…07068872025012995001

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

1.227 × 10⁹⁹(100-digit number)

12277459131080321800…14137744050025989999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.227 × 10⁹⁹(100-digit number)

12277459131080321800…14137744050025990001

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

2.455 × 10⁹⁹(100-digit number)

24554918262160643600…28275488100051979999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.455 × 10⁹⁹(100-digit number)

24554918262160643600…28275488100051980001

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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