Block #2,862,817

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 10/1/2018, 3:38:13 PM · Difficulty 11.6734 · 3,979,538 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

451b5c945146515f12ee0a2867d9e2cce63badc1f87c0dfa22748bda7eb83245

View on Chainz ↗

Height

#2,862,817

Difficulty

11.673439

Transactions

Size

1.48 KB

Version

Bits

0bac6686

Nonce

120,227,601

Timestamp

10/1/2018, 3:38:13 PM

Confirmations

3,979,538

Mined by

⛏️ P2SHAX5RJRCM88uB2oB4LzECe2dXaoVgmKfTc2

Merkle Root

0b722bab79283d00c25a550df4f495883e831226ca54036bbcc2e2c63d0c6a25

Transactions (4)

Coinbase7663a6c33d200a…0b3d3c0ba34997

1 in → 1 out7.3600 XPM110 B

AX5RJRCM…VgmKfTc2

09c892a66fb5b9…1272d3ea70f2a6

2 in → 2 out12.1600 XPM338 B

AX864m5e…FCnS52QF ATkwammm…oasHBd7n

71c7f9c7ea5bd5…842f200c2f0774

3 in → 2 out11.2700 XPM487 B

AamK1S8L…BZ9EqKQf AaU6Wjxo…t9aQerWZ

882dfb16d613cd…c13b7c1b49413f

3 in → 2 out10.7500 XPM487 B

AW3QZZmg…j2rGjUkp AJ2tLeKs…SrEG2zws

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.

2.247 × 10⁹⁸(99-digit number)

22475919184146278762…27964326697657958399

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

2.247 × 10⁹⁸(99-digit number)

22475919184146278762…27964326697657958399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.247 × 10⁹⁸(99-digit number)

22475919184146278762…27964326697657958401

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

4.495 × 10⁹⁸(99-digit number)

44951838368292557525…55928653395315916799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.495 × 10⁹⁸(99-digit number)

44951838368292557525…55928653395315916801

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

8.990 × 10⁹⁸(99-digit number)

89903676736585115051…11857306790631833599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.990 × 10⁹⁸(99-digit number)

89903676736585115051…11857306790631833601

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

1.798 × 10⁹⁹(100-digit number)

17980735347317023010…23714613581263667199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.798 × 10⁹⁹(100-digit number)

17980735347317023010…23714613581263667201

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

3.596 × 10⁹⁹(100-digit number)

35961470694634046020…47429227162527334399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.596 × 10⁹⁹(100-digit number)

35961470694634046020…47429227162527334401

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

7.192 × 10⁹⁹(100-digit number)

71922941389268092040…94858454325054668799

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 #2,862,817

Cookie Preferences