Block #58,273

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/17/2013, 7:47:51 PM · Difficulty 8.9590 · 6,767,841 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f3ce795e486f9f829c2197c7e211d680c6a1cb1478af8281c855463ead718d1a

View on Chainz ↗

Height

#58,273

Difficulty

8.958998

Transactions

Size

958 B

Version

Bits

08f580e1

Nonce

881

Timestamp

7/17/2013, 7:47:51 PM

Confirmations

6,767,841

Mined by

⛏️ P2SHAebtKwPEhgtVdMFdoMU1t2A4kMMmZNbcH4

Merkle Root

517f3ebd4ea8e18e153d8e58a7723dbc2eb34cd70f6558d4772485cd1a26627e

Transactions (3)

Coinbase8105057ac846e2…3473b435e0a1b6

1 in → 1 out12.4600 XPM110 B

AebtKwPE…MmZNbcH4

1d325852cb2263…aedd969940380b

2 in → 1 out37.4100 XPM272 B

AWragWmG…Nn3Cqmw5

5c37322ffc7fd5…2713b73cdc20e6

3 in → 2 out95.3400 XPM487 B

AR9sc9xL…8tuPfq65 AeiFXFT5…ZnTrM7yc

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.

2.762 × 10⁹¹(92-digit number)

27629769525170745502…97642502917607957499

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

2.762 × 10⁹¹(92-digit number)

27629769525170745502…97642502917607957499

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.762 × 10⁹¹(92-digit number)

27629769525170745502…97642502917607957501

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

5.525 × 10⁹¹(92-digit number)

55259539050341491004…95285005835215914999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.525 × 10⁹¹(92-digit number)

55259539050341491004…95285005835215915001

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

1.105 × 10⁹²(93-digit number)

11051907810068298200…90570011670431829999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.105 × 10⁹²(93-digit number)

11051907810068298200…90570011670431830001

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

2.210 × 10⁹²(93-digit number)

22103815620136596401…81140023340863659999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.210 × 10⁹²(93-digit number)

22103815620136596401…81140023340863660001

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

4.420 × 10⁹²(93-digit number)

44207631240273192803…62280046681727319999

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 #58,273

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