Block #3,630,578

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/5/2020, 7:46:19 PM · Difficulty 10.9043 · 3,211,886 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ad132e4384b98a7d9e5f18fd2e11386d59a0e6a440040d4578d0088fb1292e8d

View on Chainz ↗

Height

#3,630,578

Difficulty

10.904329

Transactions

Size

7.35 KB

Version

Bits

0ae78222

Nonce

136,456,213

Timestamp

4/5/2020, 7:46:19 PM

Confirmations

3,211,886

Mined by

⛏️ P2SHASiq2qtKTzQ7sbERFE8Jp8HjsgVMhmk7yL

Merkle Root

9470e1e11f5f7736e2b08b4232dfc19b284d3967a247f898793ba80a2b78fb9d

Transactions (3)

Coinbaseacd1f43f11c7c4…970eabeba3e270

1 in → 1 out8.4900 XPM109 B

ASiq2qtK…VMhmk7yL

4d2be2c199ca97…5479ec1a92eac3

61 in → 2 out500.8449 XPM6.93 KB

Ab5fFXVt…EC9k8a2d ASiq2qtK…VMhmk7yL

48a2f6c3d7f096…80ea7df5ceb7ab

1 in → 2 out6.4331 XPM226 B

ASiq2qtK…VMhmk7yL AQDRSD4c…e9prhFrA

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.

6.181 × 10⁹⁷(98-digit number)

61810703076965136532…09422061541295390719

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

6.181 × 10⁹⁷(98-digit number)

61810703076965136532…09422061541295390719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.181 × 10⁹⁷(98-digit number)

61810703076965136532…09422061541295390721

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

1.236 × 10⁹⁸(99-digit number)

12362140615393027306…18844123082590781439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.236 × 10⁹⁸(99-digit number)

12362140615393027306…18844123082590781441

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

2.472 × 10⁹⁸(99-digit number)

24724281230786054613…37688246165181562879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.472 × 10⁹⁸(99-digit number)

24724281230786054613…37688246165181562881

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

4.944 × 10⁹⁸(99-digit number)

49448562461572109226…75376492330363125759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.944 × 10⁹⁸(99-digit number)

49448562461572109226…75376492330363125761

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

9.889 × 10⁹⁸(99-digit number)

98897124923144218452…50752984660726251519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.889 × 10⁹⁸(99-digit number)

98897124923144218452…50752984660726251521

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 #3,630,578

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