Block #474,605

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/4/2014, 4:27:23 PM · Difficulty 10.4540 · 6,321,251 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7083826e6fddcb9e5d641a82f829cb0bb590a837987c4de85bf1c9ec92dfa98b

View on Chainz ↗

Height

#474,605

Difficulty

10.454029

Transactions

Size

3.71 KB

Version

Bits

0a743b3f

Nonce

206,150

Timestamp

4/4/2014, 4:27:23 PM

Confirmations

6,321,251

Mined by

⛏️ =aS>*AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

b78fc9e9b7d0afaf5435ca030b35ab890f888957a78248c7dfb24c909d22df0e

Transactions (4)

Coinbaseb9f86a8d3d4672…b6149c026f9319

1 in → 19 out9.1400 XPM709 B

AQvZBsUo…hppgRZTJ ANNg88pG…ppn21sTe ATKK7iFz…wZm46KN1 ALqxX1WA…hsKjbnXn AJtNW28X…Syb4Ph5j

99743cf75a66bc…6de839ed86b7ce

3 in → 2 out2209.8598 XPM520 B

ATbpKT2a…RCVFJnyk AdEv6dyG…BDmhwihC

1aa8c4101b13d1…17ca5ac3e04f18

3 in → 7 out19.3773 XPM625 B

AWcLGBjS…sWZwZBdr AeKNrjNj…1NEq95Ta AUHFmvnF…juaRoiLd AeqZw9yo…5K9AMCop ALrZxq5u…jReX3z9e

8b513731c91db1…2ac4717d1332ae

12 in → 2 out53.4808 XPM1.81 KB

APhZbt91…ERWP9zpq AHREN8qr…1wFsQnP4

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.

2.090 × 10⁹⁹(100-digit number)

20909092211686178777…04443015692794235039

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

2.090 × 10⁹⁹(100-digit number)

20909092211686178777…04443015692794235039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.090 × 10⁹⁹(100-digit number)

20909092211686178777…04443015692794235041

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

4.181 × 10⁹⁹(100-digit number)

41818184423372357555…08886031385588470079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.181 × 10⁹⁹(100-digit number)

41818184423372357555…08886031385588470081

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

8.363 × 10⁹⁹(100-digit number)

83636368846744715111…17772062771176940159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.363 × 10⁹⁹(100-digit number)

83636368846744715111…17772062771176940161

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

1.672 × 10¹⁰⁰(101-digit number)

16727273769348943022…35544125542353880319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.672 × 10¹⁰⁰(101-digit number)

16727273769348943022…35544125542353880321

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

3.345 × 10¹⁰⁰(101-digit number)

33454547538697886044…71088251084707760639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.345 × 10¹⁰⁰(101-digit number)

33454547538697886044…71088251084707760641

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