Block #2,176,198

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/24/2017, 9:29:48 PM · Difficulty 10.9187 · 4,663,565 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8605eef4ef56f47a57c357ddea910299abbdbee75ce9cbf7fef6865e1ec4a45c

View on Chainz ↗

Height

#2,176,198

Difficulty

10.918671

Transactions

Size

722 B

Version

Bits

0aeb2dfe

Nonce

995,535,628

Timestamp

6/24/2017, 9:29:48 PM

Confirmations

4,663,565

Mined by

⛏️ P2SHAURZwx39AUgbEn14wzL3nWRdv8v1izsce1

Merkle Root

a0b558b2ecfe79b43f5f596f1d521a8beb6637dd0156fe79afbdfc0ea2bf2efe

Transactions (2)

Coinbasef8c99326aebd3f…c6e80e0f15a4d5

1 in → 1 out8.3900 XPM110 B

AURZwx39…v1izsce1

9c2698a6be0f41…712ec11aacfb6e

3 in → 2 out1018.6157 XPM521 B

AZ7cQcwJ…NttCBkgL AXgkmXU6…MjhP8nmZ

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.

1.022 × 10⁹⁶(97-digit number)

10226813810106489177…01576365286736276479

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

1.022 × 10⁹⁶(97-digit number)

10226813810106489177…01576365286736276479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.022 × 10⁹⁶(97-digit number)

10226813810106489177…01576365286736276481

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

2.045 × 10⁹⁶(97-digit number)

20453627620212978354…03152730573472552959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.045 × 10⁹⁶(97-digit number)

20453627620212978354…03152730573472552961

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

4.090 × 10⁹⁶(97-digit number)

40907255240425956708…06305461146945105919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.090 × 10⁹⁶(97-digit number)

40907255240425956708…06305461146945105921

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

8.181 × 10⁹⁶(97-digit number)

81814510480851913416…12610922293890211839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.181 × 10⁹⁶(97-digit number)

81814510480851913416…12610922293890211841

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

1.636 × 10⁹⁷(98-digit number)

16362902096170382683…25221844587780423679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.636 × 10⁹⁷(98-digit number)

16362902096170382683…25221844587780423681

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #2,176,198

Cookie Preferences