Block #2,202,620

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 7/11/2017, 4:07:45 PM · Difficulty 10.9489 · 4,636,806 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ef106ac111f77bcb7d365e95b0ff48b04c4a0de25abed8fcd17889d4699d037c

View on Chainz ↗

Height

#2,202,620

Difficulty

10.948860

Transactions

Size

869 B

Version

Bits

0af2e882

Nonce

814,397,131

Timestamp

7/11/2017, 4:07:45 PM

Confirmations

4,636,806

Mined by

⛏️ P2SHASmvuP3NpfaLFJfCdTiwGSD8mjh3wQUZLd

Merkle Root

cd2f3fa90c2e3adc2caf8da6d8ad383d55670a2a58ac6234194a0775401eb604

Transactions (2)

Coinbase0fb18a23b59a5f…8b76d027466ae9

1 in → 1 out8.3400 XPM110 B

ASmvuP3N…h3wQUZLd

62980b247a170d…c483b44e2d24cd

4 in → 2 out776.0700 XPM668 B

Ac9Rrpcw…KXWZpRRE AV4d6E2B…JePGiR2K

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.

7.796 × 10⁹⁶(97-digit number)

77964888745112468027…69680294723577323519

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

7.796 × 10⁹⁶(97-digit number)

77964888745112468027…69680294723577323519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.796 × 10⁹⁶(97-digit number)

77964888745112468027…69680294723577323521

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

1.559 × 10⁹⁷(98-digit number)

15592977749022493605…39360589447154647039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.559 × 10⁹⁷(98-digit number)

15592977749022493605…39360589447154647041

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

3.118 × 10⁹⁷(98-digit number)

31185955498044987210…78721178894309294079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.118 × 10⁹⁷(98-digit number)

31185955498044987210…78721178894309294081

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

6.237 × 10⁹⁷(98-digit number)

62371910996089974421…57442357788618588159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.237 × 10⁹⁷(98-digit number)

62371910996089974421…57442357788618588161

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

1.247 × 10⁹⁸(99-digit number)

12474382199217994884…14884715577237176319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.247 × 10⁹⁸(99-digit number)

12474382199217994884…14884715577237176321

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

2.494 × 10⁹⁸(99-digit number)

24948764398435989768…29769431154474352639

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 #2,202,620

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