Block #1,227,223

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 9/8/2015, 10:24:23 AM · Difficulty 10.7348 · 5,580,711 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b9ccae06f0cfe2c85418e219e5e2b4587ae8c0388a30a9cb844937d55693538f

View on Chainz ↗

Height

#1,227,223

Difficulty

10.734754

Transactions

Size

1.08 KB

Version

Bits

0abc18d8

Nonce

105,442,549

Timestamp

9/8/2015, 10:24:23 AM

Confirmations

5,580,711

Mined by

⛏️ P2SHAMTbzyHbDhnhRyPNTv7YKsgQWdPsXfuc4J

Merkle Root

4b9fba6038ec2a21da1ee6f1164c7e3bee832c0d37643175677b8fec8c1f50f7

Transactions (5)

Coinbase7e0ae3256b4dd5…781965e7895cf7

1 in → 1 out8.7000 XPM109 B

AMTbzyHb…PsXfuc4J

6291378da8665f…4d93ec2ca43b79

1 in → 2 out8.6400 XPM227 B

AXrTw46X…e1dGvSFf AMT7PUbH…JwZdhDNy

b3416626a128fb…38c8f528fc1cc5

1 in → 2 out8.6400 XPM225 B

AQzGsiip…LXYjaGXj Abm88trM…RAPSwC5q

f75dc6bed1e117…4e00340a0eb8ca

1 in → 2 out8.6400 XPM227 B

AG6vNpQA…Upeast4S AcEGUXDj…JsRzHiLU

ee6bd4f80f461c…0c984f67860495

1 in → 2 out3.9814 XPM227 B

AcuM7XiJ…5uND8Jce AeDdnVL5…5J4QsW8y

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.

2.901 × 10⁹⁵(96-digit number)

29015720274626683449…21721886012775874559

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

2.901 × 10⁹⁵(96-digit number)

29015720274626683449…21721886012775874559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.901 × 10⁹⁵(96-digit number)

29015720274626683449…21721886012775874561

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

5.803 × 10⁹⁵(96-digit number)

58031440549253366898…43443772025551749119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.803 × 10⁹⁵(96-digit number)

58031440549253366898…43443772025551749121

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

1.160 × 10⁹⁶(97-digit number)

11606288109850673379…86887544051103498239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.160 × 10⁹⁶(97-digit number)

11606288109850673379…86887544051103498241

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

2.321 × 10⁹⁶(97-digit number)

23212576219701346759…73775088102206996479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.321 × 10⁹⁶(97-digit number)

23212576219701346759…73775088102206996481

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

4.642 × 10⁹⁶(97-digit number)

46425152439402693518…47550176204413992959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.642 × 10⁹⁶(97-digit number)

46425152439402693518…47550176204413992961

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

9.285 × 10⁹⁶(97-digit number)

92850304878805387037…95100352408827985919

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #1,227,223

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