Block #2,098,520

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/3/2017, 4:29:33 PM · Difficulty 10.8632 · 4,743,588 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

02f730623a5fae91cabf52e4c4526a16eb9fdaaa3aba177ef340fac490ef3ad2

View on Chainz ↗

Height

#2,098,520

Difficulty

10.863218

Transactions

Size

723 B

Version

Bits

0adcfbd3

Nonce

617,690,455

Timestamp

5/3/2017, 4:29:33 PM

Confirmations

4,743,588

Mined by

⛏️ P2SHAe6ajaskPeq4WzomsPZDQ7C3oJyJWgzJnm

Merkle Root

d2f4a3d8a35732da8378a6d1fbe5da8fa388b67d7ff22e757e782109ba12ebf8

Transactions (2)

Coinbase8e3b628d4191c7…026067135b81b9

1 in → 1 out8.4700 XPM109 B

Ae6ajask…yJWgzJnm

b0fc62afc0bdbf…405443e698503a

3 in → 2 out5299.2138 XPM523 B

AYJZkZzW…hHobhXUW AWFBSKPQ…ci3y94Wu

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.

6.055 × 10⁹⁷(98-digit number)

60558139030988064308…03263835820766740479

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

6.055 × 10⁹⁷(98-digit number)

60558139030988064308…03263835820766740479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.055 × 10⁹⁷(98-digit number)

60558139030988064308…03263835820766740481

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

1.211 × 10⁹⁸(99-digit number)

12111627806197612861…06527671641533480959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.211 × 10⁹⁸(99-digit number)

12111627806197612861…06527671641533480961

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

2.422 × 10⁹⁸(99-digit number)

24223255612395225723…13055343283066961919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.422 × 10⁹⁸(99-digit number)

24223255612395225723…13055343283066961921

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

4.844 × 10⁹⁸(99-digit number)

48446511224790451446…26110686566133923839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.844 × 10⁹⁸(99-digit number)

48446511224790451446…26110686566133923841

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

9.689 × 10⁹⁸(99-digit number)

96893022449580902893…52221373132267847679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.689 × 10⁹⁸(99-digit number)

96893022449580902893…52221373132267847681

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

1.937 × 10⁹⁹(100-digit number)

19378604489916180578…04442746264535695359

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #2,098,520

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