Block #2,468,856

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 1/12/2018, 2:49:24 AM · Difficulty 10.9601 · 4,371,020 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

513de8beab73f611a54764f478415a60a6edf65b3ff550ef3b9c0017f96f5a56

View on Chainz ↗

Height

#2,468,856

Difficulty

10.960129

Transactions

Size

2.11 KB

Version

Bits

0af5cb02

Nonce

1,023,841,330

Timestamp

1/12/2018, 2:49:24 AM

Confirmations

4,371,020

Mined by

⛏️ P2SHAHg9dqc2NXM1JFmJZ5YQnQBU7nhc8G6x86

Merkle Root

0ccdea0e56122ed23a5d2f3fc1a7d4573b4262d9fed0d673fb9e4399bee3821e

Transactions (3)

Coinbase68adb4ceacdb99…c56321bf43910e

1 in → 1 out8.3400 XPM109 B

AHg9dqc2…hc8G6x86

b96e769e507654…bac027b6c7201a

9 in → 3 out13.2501 XPM1.41 KB

AVP5wxt7…KC8D5uCL AVNDye3S…n9GfP5cZ AeQ7t6ij…7WJSTSFf

54ba543291aa1b…548a51374c6766

3 in → 2 out26.7478 XPM521 B

ASTsYNyC…CPgKMhhx AJ3bAN4P…35mxcFiF

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.

6.200 × 10⁹⁸(99-digit number)

62000165541714764497…48548101157327175679

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

6.200 × 10⁹⁸(99-digit number)

62000165541714764497…48548101157327175679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.200 × 10⁹⁸(99-digit number)

62000165541714764497…48548101157327175681

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

1.240 × 10⁹⁹(100-digit number)

12400033108342952899…97096202314654351359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.240 × 10⁹⁹(100-digit number)

12400033108342952899…97096202314654351361

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

2.480 × 10⁹⁹(100-digit number)

24800066216685905798…94192404629308702719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.480 × 10⁹⁹(100-digit number)

24800066216685905798…94192404629308702721

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

4.960 × 10⁹⁹(100-digit number)

49600132433371811597…88384809258617405439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.960 × 10⁹⁹(100-digit number)

49600132433371811597…88384809258617405441

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

9.920 × 10⁹⁹(100-digit number)

99200264866743623195…76769618517234810879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.920 × 10⁹⁹(100-digit number)

99200264866743623195…76769618517234810881

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

1.984 × 10¹⁰⁰(101-digit number)

19840052973348724639…53539237034469621759

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 #2,468,856

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