Block #2,486,704

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 1/23/2018, 5:40:34 PM · Difficulty 10.9685 · 4,357,008 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

444047e6939dcc15cb71437012f14c4cb435703b81ba595855079f5a25c35ff9

View on Chainz ↗

Height

#2,486,704

Difficulty

10.968526

Transactions

Size

2.27 KB

Version

Bits

0af7f154

Nonce

464,554,389

Timestamp

1/23/2018, 5:40:34 PM

Confirmations

4,357,008

Mined by

⛏️ P2SHALucEdk4JRivAK4dU7fdNCxjUhJJQXMkf8

Merkle Root

896eec69bc7f102695de257a5b9a94df0a9ad733bfd7215e9568cbdcd8000c65

Transactions (4)

Coinbase72b253c8915ce7…2aa3743efa5efb

1 in → 1 out8.3400 XPM110 B

ALucEdk4…JJQXMkf8

65471f2ccf0b0e…7bfb14c3dcee34

1 in → 2 out8.2900 XPM192 B

AeHPpVSr…BNjUZcPp ATTM173Y…v3RYnGyv

8d8f9a5965e79f…44b1934523f9fc

1 in → 2 out4.2800 XPM225 B

AeL8j3pn…DRmmRJ7R AMz3mUpm…bQK9yZhT

689bf82b4cd06a…aa0d1f99cddc41

11 in → 2 out4.0900 XPM1.67 KB

Af6HBJVa…GR2CnRRx AKhz71Ms…XjGCXuUC

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.

2.389 × 10⁹³(94-digit number)

23890501650944705215…78260430800138470719

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

2.389 × 10⁹³(94-digit number)

23890501650944705215…78260430800138470719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.389 × 10⁹³(94-digit number)

23890501650944705215…78260430800138470721

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

4.778 × 10⁹³(94-digit number)

47781003301889410431…56520861600276941439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.778 × 10⁹³(94-digit number)

47781003301889410431…56520861600276941441

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

9.556 × 10⁹³(94-digit number)

95562006603778820863…13041723200553882879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.556 × 10⁹³(94-digit number)

95562006603778820863…13041723200553882881

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

1.911 × 10⁹⁴(95-digit number)

19112401320755764172…26083446401107765759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.911 × 10⁹⁴(95-digit number)

19112401320755764172…26083446401107765761

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

3.822 × 10⁹⁴(95-digit number)

38224802641511528345…52166892802215531519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.822 × 10⁹⁴(95-digit number)

38224802641511528345…52166892802215531521

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

7.644 × 10⁹⁴(95-digit number)

76449605283023056690…04333785604431063039

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 #2,486,704

Cookie Preferences