Block #1,228,491

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/9/2015, 7:39:39 AM · Difficulty 10.7344 · 5,577,878 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9d0d890339b4863f74fad2253308edbf520cc78e0a214a990ee48fa23cd74a21

View on Chainz ↗

Height

#1,228,491

Difficulty

10.734402

Transactions

Size

653 B

Version

Bits

0abc01c0

Nonce

245,946,804

Timestamp

9/9/2015, 7:39:39 AM

Confirmations

5,577,878

Mined by

⛏️ P2SHARNNx11qP2PusM57Z1bdVae9XGfEAxtM7F

Merkle Root

b7d497eec9a21f54a880624e1a909b235dfe4da609ee15a90c09c897e3b15162

Transactions (3)

Coinbase965ae3c480cd39…6347dba93dd697

1 in → 1 out8.6800 XPM109 B

ARNNx11q…fEAxtM7F

054aebefa383e0…f94a4175f23046

1 in → 2 out3.1661 XPM226 B

AJv4c4QZ…W3DKmvZt AcEGUXDj…JsRzHiLU

86a46d47c98916…8b93317ab9c6e9

1 in → 2 out1.1011 XPM227 B

Af1ToaBG…B4gCoAKS AXrTw46X…e1dGvSFf

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.

2.617 × 10⁹⁷(98-digit number)

26177908939910292996…22760140525353410559

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

2.617 × 10⁹⁷(98-digit number)

26177908939910292996…22760140525353410559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.617 × 10⁹⁷(98-digit number)

26177908939910292996…22760140525353410561

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

5.235 × 10⁹⁷(98-digit number)

52355817879820585992…45520281050706821119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.235 × 10⁹⁷(98-digit number)

52355817879820585992…45520281050706821121

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

1.047 × 10⁹⁸(99-digit number)

10471163575964117198…91040562101413642239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.047 × 10⁹⁸(99-digit number)

10471163575964117198…91040562101413642241

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

2.094 × 10⁹⁸(99-digit number)

20942327151928234396…82081124202827284479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.094 × 10⁹⁸(99-digit number)

20942327151928234396…82081124202827284481

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

4.188 × 10⁹⁸(99-digit number)

41884654303856468793…64162248405654568959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.188 × 10⁹⁸(99-digit number)

41884654303856468793…64162248405654568961

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 #1,228,491

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