Block #2,513,591

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 2/10/2018, 3:27:18 AM · Difficulty 10.9788 · 4,318,467 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

58b91d60819d6ccbadb1c1522aa31cbac9299c0a11220fb0d774316968cb4d5f

View on Chainz ↗

Height

#2,513,591

Difficulty

10.978798

Transactions

Size

1.03 KB

Version

Bits

0afa927e

Nonce

729,975,137

Timestamp

2/10/2018, 3:27:18 AM

Confirmations

4,318,467

Mined by

⛏️ P2SHAXYvbGkBRxAQbFFgXuqVzhXGdRzZKv8xKA

Merkle Root

4488e6ac0440f146c09233f3e6b6036951a9f5857c01ce838e5e25f8efc6eed5

Transactions (3)

Coinbase6172c489327c88…d38a8b696c1c27

1 in → 1 out8.3000 XPM109 B

AXYvbGkB…zZKv8xKA

f711de9f140f9f…a6219ddb63072c

2 in → 2 out13.3454 XPM372 B

AcpKwKfN…6qjP7EVR AFyjXWUs…dLGWmqRU

88aa1c7d5ec525…8116a0833af247

3 in → 2 out10.8700 XPM488 B

AQ3b5yLz…ob4a1WRC AYMtuoYy…7yNhdSiV

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.

1.447 × 10⁹³(94-digit number)

14477277518159849548…20236682125463114019

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

1.447 × 10⁹³(94-digit number)

14477277518159849548…20236682125463114019

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.447 × 10⁹³(94-digit number)

14477277518159849548…20236682125463114021

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

2.895 × 10⁹³(94-digit number)

28954555036319699096…40473364250926228039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.895 × 10⁹³(94-digit number)

28954555036319699096…40473364250926228041

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

5.790 × 10⁹³(94-digit number)

57909110072639398192…80946728501852456079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.790 × 10⁹³(94-digit number)

57909110072639398192…80946728501852456081

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

1.158 × 10⁹⁴(95-digit number)

11581822014527879638…61893457003704912159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.158 × 10⁹⁴(95-digit number)

11581822014527879638…61893457003704912161

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

2.316 × 10⁹⁴(95-digit number)

23163644029055759276…23786914007409824319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.316 × 10⁹⁴(95-digit number)

23163644029055759276…23786914007409824321

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

4.632 × 10⁹⁴(95-digit number)

46327288058111518553…47573828014819648639

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 #2,513,591

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