Block #448,322

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/17/2014, 8:18:33 PM · Difficulty 10.3685 · 6,348,238 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d66fc6e894d0ef1d66eedf84f02b957684db0372758ea4a154868c1346550c9e

View on Chainz ↗

Height

#448,322

Difficulty

10.368508

Transactions

Size

2.41 KB

Version

Bits

0a5e5685

Nonce

130,987

Timestamp

3/17/2014, 8:18:33 PM

Confirmations

6,348,238

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

8c0da4ca744e73d679ee88c80ea16d84b277296347d7bddc355164a17f2d54f7

Transactions (4)

Coinbase00ab0a5e4d9d7d…dea0d68b55ff0d

1 in → 1 out9.3300 XPM110 B

AeKNrjNj…1NEq95Ta

e5561ad1c9db85…db74876a4e54c0

8 in → 21 out65.4169 XPM1.63 KB

ALi2Y4yi…NcukCRyt ANknLyfs…aXUtaqAc AZHEpaqf…MxbjTDc5 Aao9p1b1…7FLAEmZp Abfxu9pR…KmBFxFwg

576f5a648546e4…c8b3f6e3fade0c

1 in → 2 out7.7365 XPM226 B

AHWvXauM…oCGvjfaC AV1Ea59t…YbgD7v2o

6c961eeacf27c0…b6b1cde2c5d8ad

2 in → 2 out1.3650 XPM374 B

APCza2xF…NYW1bK7F AWMYVpvn…37sjQv37

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.

9.002 × 10⁹²(93-digit number)

90021770264485900474…85460484290218573579

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

9.002 × 10⁹²(93-digit number)

90021770264485900474…85460484290218573579

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.002 × 10⁹²(93-digit number)

90021770264485900474…85460484290218573581

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

1.800 × 10⁹³(94-digit number)

18004354052897180094…70920968580437147159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.800 × 10⁹³(94-digit number)

18004354052897180094…70920968580437147161

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

3.600 × 10⁹³(94-digit number)

36008708105794360189…41841937160874294319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.600 × 10⁹³(94-digit number)

36008708105794360189…41841937160874294321

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

7.201 × 10⁹³(94-digit number)

72017416211588720379…83683874321748588639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.201 × 10⁹³(94-digit number)

72017416211588720379…83683874321748588641

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

1.440 × 10⁹⁴(95-digit number)

14403483242317744075…67367748643497177279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.440 × 10⁹⁴(95-digit number)

14403483242317744075…67367748643497177281

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