Block #226,971

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/25/2013, 2:15:16 PM · Difficulty 9.9361 · 6,600,258 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

43edd645b00042601a7a43107e4071e29cbe0e5cde1d02cd5e39a70db34c9e9b

View on Chainz ↗

Height

#226,971

Difficulty

9.936113

Transactions

Size

2.27 KB

Version

Bits

09efa516

Nonce

4,975

Timestamp

10/25/2013, 2:15:16 PM

Confirmations

6,600,258

Mined by

⛏️ P2SHAZh37xLoZAaGvZ332vYhsgYFo5ADD1wQTs

Merkle Root

748491b047ca0ec643b4fca77ebb6feda056e77bff22dcb99b8854e2417d8b9a

Transactions (4)

Coinbase6e2462271cf93a…1972e13c90ed95

1 in → 1 out10.1500 XPM109 B

AZh37xLo…ADD1wQTs

9a0a52a98c8769…28ad9527813241

11 in → 2 out50.2084 XPM1.67 KB

AZAyWY3s…qz5Vame5 AHvMbbnQ…WyLkoemD

5e4b08d63e29b5…370823860ac8ea

1 in → 1 out10.1000 XPM192 B

AREJRekG…a8dWbE8j

cf6ed37e8cfff9…b5fe90dafc21fd

1 in → 2 out2.1093 XPM225 B

AckR11An…ZSHgAfcD AdWp2YRv…FDtt217a

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.

1.221 × 10⁹³(94-digit number)

12211733315821914305…25060364888044730239

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

1.221 × 10⁹³(94-digit number)

12211733315821914305…25060364888044730239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.221 × 10⁹³(94-digit number)

12211733315821914305…25060364888044730241

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

2.442 × 10⁹³(94-digit number)

24423466631643828611…50120729776089460479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.442 × 10⁹³(94-digit number)

24423466631643828611…50120729776089460481

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

4.884 × 10⁹³(94-digit number)

48846933263287657222…00241459552178920959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.884 × 10⁹³(94-digit number)

48846933263287657222…00241459552178920961

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

9.769 × 10⁹³(94-digit number)

97693866526575314444…00482919104357841919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.769 × 10⁹³(94-digit number)

97693866526575314444…00482919104357841921

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

1.953 × 10⁹⁴(95-digit number)

19538773305315062888…00965838208715683839

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 #226,971

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