Block #2,833,415

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 9/10/2018, 5:35:33 PM · Difficulty 11.7160 · 4,005,962 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b1f7f72d186d2c9d5e8238535fa229315cb9bc04c420d9772f9b6a8b9f201195

View on Chainz ↗

Height

#2,833,415

Difficulty

11.716023

Transactions

Size

847 B

Version

Bits

0bb74d45

Nonce

1,023,625,034

Timestamp

9/10/2018, 5:35:33 PM

Confirmations

4,005,962

Mined by

⛏️ P2SHAPdU3XcvzmgN6oa5Z7rzGamerCZpYKHg7o

Merkle Root

99c689a416bf9aca3d323e2072ea4277c68a409c037c6fc059b94f963b8e4b29

Transactions (3)

Coinbaseb99b23fc589415…29b9c7f322e1d0

1 in → 1 out7.2900 XPM109 B

APdU3Xcv…ZpYKHg7o

f32e2acb4291c5…41851d7a0276d0

2 in → 2 out14.5300 XPM307 B

AMANjgG3…fDX1sBur AKfN5ELc…A3YNDXZ8

c73526e42bcf16…d12a2bfd7d4258

2 in → 2 out11.7900 XPM339 B

AW3QZZmg…j2rGjUkp AQS5qc4c…6ffKzMdV

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.

9.496 × 10⁹⁸(99-digit number)

94968347495504993058…17163658413902725119

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

9.496 × 10⁹⁸(99-digit number)

94968347495504993058…17163658413902725119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.496 × 10⁹⁸(99-digit number)

94968347495504993058…17163658413902725121

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

1.899 × 10⁹⁹(100-digit number)

18993669499100998611…34327316827805450239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.899 × 10⁹⁹(100-digit number)

18993669499100998611…34327316827805450241

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

3.798 × 10⁹⁹(100-digit number)

37987338998201997223…68654633655610900479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.798 × 10⁹⁹(100-digit number)

37987338998201997223…68654633655610900481

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

7.597 × 10⁹⁹(100-digit number)

75974677996403994446…37309267311221800959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.597 × 10⁹⁹(100-digit number)

75974677996403994446…37309267311221800961

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

1.519 × 10¹⁰⁰(101-digit number)

15194935599280798889…74618534622443601919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.519 × 10¹⁰⁰(101-digit number)

15194935599280798889…74618534622443601921

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

3.038 × 10¹⁰⁰(101-digit number)

30389871198561597778…49237069244887203839

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 #2,833,415

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