Block #503,524

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/21/2014, 3:47:20 AM · Difficulty 10.8089 · 6,333,096 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

85ad9d26d4c86a8a8cad225684dde62f5292819591d891ae186eca8aec86b23a

View on Chainz ↗

Height

#503,524

Difficulty

10.808859

Transactions

Size

1.08 KB

Version

Bits

0acf1168

Nonce

517,239,438

Timestamp

4/21/2014, 3:47:20 AM

Confirmations

6,333,096

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

976612cb338ca9f60c3b6fa28619ccc055279d849d9e0636b326ca8ea9fe76a5

Transactions (5)

Coinbase9e01b12809cc81…6488fdb1432458

1 in → 1 out8.5900 XPM116 B

AbwWkWZt…kawDhufa

205d34ed22b6ae…714ad6a8983601

1 in → 2 out8.5500 XPM225 B

AKXJKYwJ…jFWbpUTe AYMW7uyc…YejwWmN3

044880b1ea7971…7a2091666cf19d

1 in → 2 out8.5500 XPM226 B

AQBZitg7…LxgpvhqV ASpPXhrL…i2TUy87G

e4d1e5d1ef591e…f01b3c75491226

1 in → 2 out8.5500 XPM227 B

AYhKsPNY…LTcm9HRQ AM8GuxnN…AfjbhWoV

62dcf20c59ebc6…718e45094daec1

1 in → 2 out6.4324 XPM225 B

AGzuhBha…xzp4nRg2 AR765XcW…PRMDQ8Qy

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.

5.419 × 10⁹⁸(99-digit number)

54198671804499672851…28814370566793182719

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

5.419 × 10⁹⁸(99-digit number)

54198671804499672851…28814370566793182719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.419 × 10⁹⁸(99-digit number)

54198671804499672851…28814370566793182721

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

1.083 × 10⁹⁹(100-digit number)

10839734360899934570…57628741133586365439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.083 × 10⁹⁹(100-digit number)

10839734360899934570…57628741133586365441

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

2.167 × 10⁹⁹(100-digit number)

21679468721799869140…15257482267172730879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.167 × 10⁹⁹(100-digit number)

21679468721799869140…15257482267172730881

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

4.335 × 10⁹⁹(100-digit number)

43358937443599738281…30514964534345461759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.335 × 10⁹⁹(100-digit number)

43358937443599738281…30514964534345461761

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

8.671 × 10⁹⁹(100-digit number)

86717874887199476563…61029929068690923519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.671 × 10⁹⁹(100-digit number)

86717874887199476563…61029929068690923521

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

Block #503,524

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