Block #2,678,230

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/26/2018, 3:58:29 AM · Difficulty 11.6943 · 4,154,548 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

dea4ff43abaebe2e768275c04a7415b7c4e5fa19f6f9c1197bae16f334fb5e34

View on Chainz ↗

Height

#2,678,230

Difficulty

11.694340

Transactions

Size

2.32 KB

Version

Bits

0bb1c03d

Nonce

237,004,035

Timestamp

5/26/2018, 3:58:29 AM

Confirmations

4,154,548

Mined by

⛏️ P2SHAVAtbU19WWhHL3jbi3qUKfCHLX42X4yUzJ

Merkle Root

c08c7701c807d6ce1221ecd1fe3a179cc2915272b321b4e2a913585ab371c9a2

Transactions (5)

Coinbase9543b8208bcc9c…c7277059149c6d

1 in → 1 out7.3500 XPM109 B

AVAtbU19…42X4yUzJ

fef8f7879be56c…72266304bff7c0

2 in → 2 out14.5700 XPM306 B

AZc8kSMn…2SuivEGm AKD9LeNP…bQTn8mEf

7dfc218c47a620…d2921593a11a20

2 in → 2 out11.8800 XPM341 B

AQ7S9cWe…rDsLcCRa AbMfYdnk…4eahmS56

788fb6bd05bc41…1c8c31b7304951

2 in → 2 out11.8500 XPM341 B

ASQ5SGd2…Bk3wNRzc AH7oVtQW…eQzY19jY

6e9bb421126bb3…4ba950bb4579ac

8 in → 1 out10.0000 XPM1.17 KB

AW3QZZmg…j2rGjUkp

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.

6.611 × 10⁹³(94-digit number)

66111090939748637739…76978435007954071039

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

6.611 × 10⁹³(94-digit number)

66111090939748637739…76978435007954071039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.611 × 10⁹³(94-digit number)

66111090939748637739…76978435007954071041

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

1.322 × 10⁹⁴(95-digit number)

13222218187949727547…53956870015908142079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.322 × 10⁹⁴(95-digit number)

13222218187949727547…53956870015908142081

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

2.644 × 10⁹⁴(95-digit number)

26444436375899455095…07913740031816284159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.644 × 10⁹⁴(95-digit number)

26444436375899455095…07913740031816284161

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

5.288 × 10⁹⁴(95-digit number)

52888872751798910191…15827480063632568319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.288 × 10⁹⁴(95-digit number)

52888872751798910191…15827480063632568321

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

1.057 × 10⁹⁵(96-digit number)

10577774550359782038…31654960127265136639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.057 × 10⁹⁵(96-digit number)

10577774550359782038…31654960127265136641

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

2.115 × 10⁹⁵(96-digit number)

21155549100719564076…63309920254530273279

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 #2,678,230

Cookie Preferences