Block #3,085,414

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 3/9/2019, 12:51:51 PM · Difficulty 11.0322 · 3,751,341 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

53a4bfd9fa6d7c6c8ec3c6cf42c1b3e59584b85f302cd2700252efb014756fa5

View on Chainz ↗

Height

#3,085,414

Difficulty

11.032155

Transactions

Size

2.96 KB

Version

Bits

0b083b4f

Nonce

1,267,537,931

Timestamp

3/9/2019, 12:51:51 PM

Confirmations

3,751,341

Mined by

⛏️ VAbXwmGxDc5ZxwPwgT1QckjRUmF4XXYP765

Merkle Root

82fb5fc14ca88556846c8c610eacb5b2e735bdd8b00a21a5550df1a19ffbd459

Transactions (4)

Coinbase1d9da527a8a503…21353e1485f984

1 in → 1 out8.2500 XPM110 B

AbXwmGxD…4XXYP765

6250f5b5574d63…34315a39424bea

14 in → 2 out2521.2629 XPM2.09 KB

AZQgL5kt…6NE43uZs AGWq4Yi5…fMiA32Jn

5a9cc19e3ca7a5…7c87c438f2a420

2 in → 2 out14.6700 XPM339 B

AamK1S8L…BZ9EqKQf APzTSpJN…BW8YwoBU

bb98972a046faf…52a40d67b7564d

2 in → 2 out12.8800 XPM341 B

AaHsEQd6…A22sKQ7o AUtp67T1…GVPvmF2N

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.

2.485 × 10⁹⁷(98-digit number)

24855352916759659378…74589409055354593279

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

2.485 × 10⁹⁷(98-digit number)

24855352916759659378…74589409055354593279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.485 × 10⁹⁷(98-digit number)

24855352916759659378…74589409055354593281

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

4.971 × 10⁹⁷(98-digit number)

49710705833519318757…49178818110709186559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.971 × 10⁹⁷(98-digit number)

49710705833519318757…49178818110709186561

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

9.942 × 10⁹⁷(98-digit number)

99421411667038637515…98357636221418373119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.942 × 10⁹⁷(98-digit number)

99421411667038637515…98357636221418373121

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

1.988 × 10⁹⁸(99-digit number)

19884282333407727503…96715272442836746239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.988 × 10⁹⁸(99-digit number)

19884282333407727503…96715272442836746241

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

3.976 × 10⁹⁸(99-digit number)

39768564666815455006…93430544885673492479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.976 × 10⁹⁸(99-digit number)

39768564666815455006…93430544885673492481

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

7.953 × 10⁹⁸(99-digit number)

79537129333630910012…86861089771346984959

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 #3,085,414

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