Block #442,915

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/14/2014, 5:07:33 AM · Difficulty 10.3426 · 6,382,786 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

85c489bab62aef9204cdc492c601f75ae9983815f309e2b4506d66d7fd8cb588

View on Chainz ↗

Height

#442,915

Difficulty

10.342626

Transactions

Size

2.01 KB

Version

Bits

0a57b658

Nonce

89,938

Timestamp

3/14/2014, 5:07:33 AM

Confirmations

6,382,786

Mined by

⛏️ #aS"AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

0428b7c5bd8d91bb6db81b71eb74f1bc246ac181c4b4fc840fa600496fc95fa3

Transactions (4)

Coinbaseda97f4de3b75b7…ff033cf3c6f85e

1 in → 23 out9.3300 XPM845 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AScAzqGc…BZ6tV1vJ AGKhfQo2…h7fBXLX6 ALqxX1WA…hsKjbnXn

1fe2a9f58a8c8b…cca3d95d62f1ad

4 in → 2 out10.1019 XPM669 B

AQK9sDmr…qPQk9kcY AM9gxnSA…EBSVq4PJ

0b79e276ba705f…24ff0e7ada98d8

1 in → 2 out7.2048 XPM226 B

AcNfyX9t…hT5WFcoz APf7RSh4…EebND2o2

d4816badce03ff…09aaac1e7e1879

1 in → 2 out4.1995 XPM225 B

AdpsxmtJ…ZWfmvRK9 ASNXRvQM…4yrumW2F

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.

9.817 × 10⁹⁴(95-digit number)

98179670208021363898…01445426376357157619

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

9.817 × 10⁹⁴(95-digit number)

98179670208021363898…01445426376357157619

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.817 × 10⁹⁴(95-digit number)

98179670208021363898…01445426376357157621

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

1.963 × 10⁹⁵(96-digit number)

19635934041604272779…02890852752714315239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.963 × 10⁹⁵(96-digit number)

19635934041604272779…02890852752714315241

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

3.927 × 10⁹⁵(96-digit number)

39271868083208545559…05781705505428630479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.927 × 10⁹⁵(96-digit number)

39271868083208545559…05781705505428630481

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

7.854 × 10⁹⁵(96-digit number)

78543736166417091119…11563411010857260959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.854 × 10⁹⁵(96-digit number)

78543736166417091119…11563411010857260961

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

1.570 × 10⁹⁶(97-digit number)

15708747233283418223…23126822021714521919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.570 × 10⁹⁶(97-digit number)

15708747233283418223…23126822021714521921

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 #442,915

Cookie Preferences