Block #1,226,017

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/7/2015, 1:28:53 PM · Difficulty 10.7373 · 5,584,304 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c55806ab295c5822f85ec3a11af532ac0e6e26bf9b2a51a7b281b3c05a1c912f

View on Chainz ↗

Height

#1,226,017

Difficulty

10.737278

Transactions

Size

1.01 KB

Version

Bits

0abcbe3b

Nonce

944,042,930

Timestamp

9/7/2015, 1:28:53 PM

Confirmations

5,584,304

Mined by

⛏️ P2SHAJCEY9yyy2DERzsA24UUtHTMGPtg97E6zm

Merkle Root

5dba7042dad25dd2b3e0813662aec49973441e424a58354e826a370a9b4389b3

Transactions (4)

Coinbaseb6104ce5799716…256cd88375394f

1 in → 1 out8.6900 XPM116 B

AJCEY9yy…tg97E6zm

4a918e718ce05c…efcc701a3e7f69

2 in → 2 out15.1072 XPM373 B

ARfx2wNb…gxiEUAHB AaC4DYoE…ucFW1A8X

28e0620ab68ed9…acd2d94db74f2f

1 in → 2 out8.6400 XPM227 B

AXviEZG8…SWVFpLqX AU4f4km9…u8UnNcJ8

5615c56a174e56…716b09c1328cde

1 in → 2 out8.6400 XPM226 B

AWfp21WJ…kreLfGhJ AcuM7XiJ…5uND8Jce

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.

2.259 × 10⁹⁵(96-digit number)

22597171064183267059…53903966190974614669

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

2.259 × 10⁹⁵(96-digit number)

22597171064183267059…53903966190974614669

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.259 × 10⁹⁵(96-digit number)

22597171064183267059…53903966190974614671

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

4.519 × 10⁹⁵(96-digit number)

45194342128366534119…07807932381949229339

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.519 × 10⁹⁵(96-digit number)

45194342128366534119…07807932381949229341

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

9.038 × 10⁹⁵(96-digit number)

90388684256733068239…15615864763898458679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.038 × 10⁹⁵(96-digit number)

90388684256733068239…15615864763898458681

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

1.807 × 10⁹⁶(97-digit number)

18077736851346613647…31231729527796917359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.807 × 10⁹⁶(97-digit number)

18077736851346613647…31231729527796917361

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

3.615 × 10⁹⁶(97-digit number)

36155473702693227295…62463459055593834719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.615 × 10⁹⁶(97-digit number)

36155473702693227295…62463459055593834721

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 #1,226,017

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