Block #474,038

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/4/2014, 7:57:07 AM · Difficulty 10.4471 · 6,324,999 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

36331440c36f0c8ebbafc00a61fab23fe1c2498826f308ffb095eb34ee34cfa5

View on Chainz ↗

Height

#474,038

Difficulty

10.447150

Transactions

Size

1.31 KB

Version

Bits

0a727865

Nonce

43,190

Timestamp

4/4/2014, 7:57:07 AM

Confirmations

6,324,999

Mined by

AGz9gyZWgxBxAyVrKrWDzMw21kbo8NYQpw

Merkle Root

c452ee7433378239dbaa02c98e155d6766d7e7f930524a8c83648420a2620fa2

Transactions (2)

Coinbasedece503c10c87f…636539462dc138

1 in → 22 out9.1600 XPM811 B

AGz9gyZW…bo8NYQpw AdFLJFhb…bsaVkAyh AUzEPJFG…kYkA5U9V ASgUri65…C7NLcyBg AMW1p9oT…2TzdaZxH

edd037e6db9cef…9264b45e2294db

2 in → 6 out18.3500 XPM441 B

AaTefDEf…9zM4GxnE AWCifDd1…Nv6sojqc AeYjcQm6…JX7NwXHM AeKNrjNj…1NEq95Ta AcnLa8bL…JuTjcdbL

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.

2.474 × 10⁹⁸(99-digit number)

24741307969373366189…40008843192924899039

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

2.474 × 10⁹⁸(99-digit number)

24741307969373366189…40008843192924899039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.474 × 10⁹⁸(99-digit number)

24741307969373366189…40008843192924899041

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

4.948 × 10⁹⁸(99-digit number)

49482615938746732379…80017686385849798079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.948 × 10⁹⁸(99-digit number)

49482615938746732379…80017686385849798081

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

9.896 × 10⁹⁸(99-digit number)

98965231877493464759…60035372771699596159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.896 × 10⁹⁸(99-digit number)

98965231877493464759…60035372771699596161

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

1.979 × 10⁹⁹(100-digit number)

19793046375498692951…20070745543399192319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.979 × 10⁹⁹(100-digit number)

19793046375498692951…20070745543399192321

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

3.958 × 10⁹⁹(100-digit number)

39586092750997385903…40141491086798384639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.958 × 10⁹⁹(100-digit number)

39586092750997385903…40141491086798384641

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