Block #455,189

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/22/2014, 10:25:16 AM · Difficulty 10.4041 · 6,351,891 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

dd3a1129cff91bfbc924de7ae4e620c5ed1eea15401d033ec1c4c601178e210c

View on Chainz ↗

Height

#455,189

Difficulty

10.404093

Transactions

Size

1.36 KB

Version

Bits

0a6772a3

Nonce

43,640

Timestamp

3/22/2014, 10:25:16 AM

Confirmations

6,351,891

Mined by

⛏️ P2SHARrYdybwbtwWaFkWbsV9pYnZj6pAampUSJ

Merkle Root

01921f293da8d5a81054b23527d850649e96e0fc20b83af6554c7d12eab5080b

Transactions (3)

Coinbase22eba443b7aaad…0ba679d9d98684

1 in → 1 out9.2500 XPM111 B

ARrYdybw…pAampUSJ

9d3e3294e7656c…9fd5381b09c086

2 in → 2 out0.9935 XPM374 B

AeM2JAGH…djCFddyX APxouLvi…xkwW73kF

f6d13bc8fbe856…09ba4773df86c6

5 in → 2 out4.0243 XPM820 B

AKkrgzeU…T5UV3nsF ASV1GSNH…dh74oypV

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.

8.672 × 10⁹⁶(97-digit number)

86727656872835001098…35523676137012502699

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

8.672 × 10⁹⁶(97-digit number)

86727656872835001098…35523676137012502699

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.672 × 10⁹⁶(97-digit number)

86727656872835001098…35523676137012502701

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

1.734 × 10⁹⁷(98-digit number)

17345531374567000219…71047352274025005399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.734 × 10⁹⁷(98-digit number)

17345531374567000219…71047352274025005401

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

3.469 × 10⁹⁷(98-digit number)

34691062749134000439…42094704548050010799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.469 × 10⁹⁷(98-digit number)

34691062749134000439…42094704548050010801

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

6.938 × 10⁹⁷(98-digit number)

69382125498268000878…84189409096100021599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.938 × 10⁹⁷(98-digit number)

69382125498268000878…84189409096100021601

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

1.387 × 10⁹⁸(99-digit number)

13876425099653600175…68378818192200043199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.387 × 10⁹⁸(99-digit number)

13876425099653600175…68378818192200043201

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 #455,189

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