Block #2,130,030

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/24/2017, 3:52:40 AM · Difficulty 10.9094 · 4,710,152 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9edefb3ab3b469d5d23e7ee69acc7afb31411a6d851d576531fa2bb083d16341

View on Chainz ↗

Height

#2,130,030

Difficulty

10.909392

Transactions

Size

426 B

Version

Bits

0ae8cde6

Nonce

681,083,916

Timestamp

5/24/2017, 3:52:40 AM

Confirmations

4,710,152

Mined by

⛏️ P2SHAVCGmHVJ82vsu6ERqv6W1rWWVKQpysBWMw

Merkle Root

6563115ba7c125b936db9c6fc1b294f7c65fcf005979a49389cf2a3de0c69cde

Transactions (2)

Coinbased34b09364c498c…1184625fa1eab2

1 in → 1 out8.4000 XPM110 B

AVCGmHVJ…QpysBWMw

a36d7fb9512da9…e8d72bf4050dba

1 in → 2 out200771.9525 XPM226 B

AKSPLsgb…syzJxKet AWSpM1vT…ukZRfqjD

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.

3.506 × 10⁹³(94-digit number)

35061267608713343866…29097103216114431999

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

3.506 × 10⁹³(94-digit number)

35061267608713343866…29097103216114431999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.506 × 10⁹³(94-digit number)

35061267608713343866…29097103216114432001

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

7.012 × 10⁹³(94-digit number)

70122535217426687732…58194206432228863999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.012 × 10⁹³(94-digit number)

70122535217426687732…58194206432228864001

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

1.402 × 10⁹⁴(95-digit number)

14024507043485337546…16388412864457727999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.402 × 10⁹⁴(95-digit number)

14024507043485337546…16388412864457728001

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

2.804 × 10⁹⁴(95-digit number)

28049014086970675093…32776825728915455999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.804 × 10⁹⁴(95-digit number)

28049014086970675093…32776825728915456001

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

5.609 × 10⁹⁴(95-digit number)

56098028173941350186…65553651457830911999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.609 × 10⁹⁴(95-digit number)

56098028173941350186…65553651457830912001

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

1.121 × 10⁹⁵(96-digit number)

11219605634788270037…31107302915661823999

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 #2,130,030

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