Block #525,313

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/4/2014, 4:56:59 PM · Difficulty 10.8794 · 6,283,673 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

49e12940e96b27eef2e71b075e3f05a1ea1cf53f2a3544810a61fa26d583e579

View on Chainz ↗

Height

#525,313

Difficulty

10.879381

Transactions

Size

868 B

Version

Bits

0ae11f1e

Nonce

150,805

Timestamp

5/4/2014, 4:56:59 PM

Confirmations

6,283,673

Mined by

⛏️ aAGz9gyZWgxBxAyVrKrWDzMw21kbo8NYQpw

Merkle Root

359c5ea54ca9dd5cf21485870a98f0451ba87865da0f23d41c51b7a046feb1c0

Transactions (1)

Coinbase359c5ea54ca9dd…51b7a046feb1c0

1 in → 21 out8.4400 XPM777 B

AGz9gyZW…bo8NYQpw AUFKXvnz…342ApNcm AUzEPJFG…kYkA5U9V ASgUri65…C7NLcyBg ATp4jJhs…TbSgR8Qb

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.

1.447 × 10⁹⁶(97-digit number)

14473045598709879088…59379547887222958399

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

1.447 × 10⁹⁶(97-digit number)

14473045598709879088…59379547887222958399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.447 × 10⁹⁶(97-digit number)

14473045598709879088…59379547887222958401

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

2.894 × 10⁹⁶(97-digit number)

28946091197419758177…18759095774445916799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.894 × 10⁹⁶(97-digit number)

28946091197419758177…18759095774445916801

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

5.789 × 10⁹⁶(97-digit number)

57892182394839516355…37518191548891833599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.789 × 10⁹⁶(97-digit number)

57892182394839516355…37518191548891833601

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

1.157 × 10⁹⁷(98-digit number)

11578436478967903271…75036383097783667199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.157 × 10⁹⁷(98-digit number)

11578436478967903271…75036383097783667201

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

2.315 × 10⁹⁷(98-digit number)

23156872957935806542…50072766195567334399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.315 × 10⁹⁷(98-digit number)

23156872957935806542…50072766195567334401

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 #525,313

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