Block #408,921

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/18/2014, 1:00:00 AM · Difficulty 10.4245 · 6,385,626 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

36ae44ad978a6bdf23787453af09185a64dc46d05b2426cbb7d5bf02bf2e58ff

View on Chainz ↗

Height

#408,921

Difficulty

10.424468

Transactions

Size

1.08 KB

Version

Bits

0a6ca9ef

Nonce

528,315

Timestamp

2/18/2014, 1:00:00 AM

Confirmations

6,385,626

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

5aad00529c626cf5ae0354927d00ee3da70aff0747c18c32638b4063702ccb32

Transactions (5)

Coinbasebe813c7cd2a32d…7e094360c6bdca

1 in → 1 out9.2300 XPM116 B

AbwWkWZt…kawDhufa

07450fea34941e…75f7c213234bc2

1 in → 2 out8.1320 XPM225 B

Aahdy5RD…mWJ7fAkz AWWg5w3k…Mb1bnxL8

600959ef6ebb6e…546b0edc5d1b42

1 in → 2 out7.1214 XPM225 B

AZCCb46c…nege1vh6 AajzSvte…V7BMBiST

898e2bf5fb9605…ea67c7e24f3b39

1 in → 2 out6.0549 XPM225 B

ANmFDMVA…qn7iQyRN AdQnBKM4…zozpvqnU

ed9a253cf87bd9…dcc0342bbf3f26

1 in → 2 out3.1136 XPM225 B

AdhUErGY…P6SsFaVU AVQ2SpSX…B7h9T3os

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.

4.551 × 10¹⁰¹(102-digit number)

45515573474869170498…47696009995248701439

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

4.551 × 10¹⁰¹(102-digit number)

45515573474869170498…47696009995248701439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.551 × 10¹⁰¹(102-digit number)

45515573474869170498…47696009995248701441

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

9.103 × 10¹⁰¹(102-digit number)

91031146949738340997…95392019990497402879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.103 × 10¹⁰¹(102-digit number)

91031146949738340997…95392019990497402881

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

1.820 × 10¹⁰²(103-digit number)

18206229389947668199…90784039980994805759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.820 × 10¹⁰²(103-digit number)

18206229389947668199…90784039980994805761

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

3.641 × 10¹⁰²(103-digit number)

36412458779895336398…81568079961989611519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.641 × 10¹⁰²(103-digit number)

36412458779895336398…81568079961989611521

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

7.282 × 10¹⁰²(103-digit number)

72824917559790672797…63136159923979223039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.282 × 10¹⁰²(103-digit number)

72824917559790672797…63136159923979223041

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