Block #2,173,908

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 6/23/2017, 3:33:33 PM · Difficulty 10.9103 · 4,657,935 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4b59e363d6c2b19d1e6a1ebcee32cfaff32a47acad82bfdf5fb36851a9e2cb59

View on Chainz ↗

Height

#2,173,908

Difficulty

10.910263

Transactions

Size

915 B

Version

Bits

0ae90701

Nonce

1,932,439,423

Timestamp

6/23/2017, 3:33:33 PM

Confirmations

4,657,935

Mined by

⛏️ P2SHAPyuD9ZevqbfZv8n2hd2foWWnh9RcbF8pm

Merkle Root

cdece6c8cecd2268a79f244aeff34ec7fcbe8018ea09ad5cf7dfbdbf4fb69e1b

Transactions (3)

Coinbasedd4ff0a6324e10…154a96a940a1b6

1 in → 1 out8.4100 XPM110 B

APyuD9Ze…9RcbF8pm

c9561c445d1642…10d24fd7b6655f

3 in → 2 out444.0840 XPM522 B

ASHcCuHZ…RVPXpG5s AHEMYbcK…Nj5M57LC

aa0edcb37a41d1…36af9ad3e23586

1 in → 2 out8.3900 XPM191 B

AWWSqvFW…mpCmjJKy ANP9Msm5…tnnC3N8T

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.

6.910 × 10⁹⁸(99-digit number)

69107560621648240523…33701619243730534399

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

6.910 × 10⁹⁸(99-digit number)

69107560621648240523…33701619243730534399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.910 × 10⁹⁸(99-digit number)

69107560621648240523…33701619243730534401

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

1.382 × 10⁹⁹(100-digit number)

13821512124329648104…67403238487461068799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.382 × 10⁹⁹(100-digit number)

13821512124329648104…67403238487461068801

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

2.764 × 10⁹⁹(100-digit number)

27643024248659296209…34806476974922137599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.764 × 10⁹⁹(100-digit number)

27643024248659296209…34806476974922137601

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

5.528 × 10⁹⁹(100-digit number)

55286048497318592418…69612953949844275199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.528 × 10⁹⁹(100-digit number)

55286048497318592418…69612953949844275201

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

1.105 × 10¹⁰⁰(101-digit number)

11057209699463718483…39225907899688550399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.105 × 10¹⁰⁰(101-digit number)

11057209699463718483…39225907899688550401

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

2.211 × 10¹⁰⁰(101-digit number)

22114419398927436967…78451815799377100799

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 #2,173,908

Cookie Preferences