Block #2,057,122

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 4/5/2017, 4:46:40 PM · Difficulty 10.8284 · 4,760,193 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d553548781bfe0fb8f350c340b59a07ecec076fa146a9fb778107bcde89e8d6c

View on Chainz ↗

Height

#2,057,122

Difficulty

10.828421

Transactions

Size

723 B

Version

Bits

0ad4136d

Nonce

42,968,503

Timestamp

4/5/2017, 4:46:40 PM

Confirmations

4,760,193

Mined by

⛏️ P2SHAP3coRpEwKq4JrUh9cFdHdWcaE32o2UBMJ

Merkle Root

0865146389486dfc86923c8f7e7a49e06bb88fe5d603e7fd13b9898994939d16

Transactions (2)

Coinbase1ce1890aa33506…a99618572423cd

1 in → 1 out8.5200 XPM109 B

AP3coRpE…32o2UBMJ

db9c8bcf193385…b384bbff772bcd

3 in → 2 out17.0170 XPM523 B

AdvLfhqF…YUuRFQZL AbcJLrRE…dGiLpuPP

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.

7.550 × 10⁹⁶(97-digit number)

75501338700011124349…97865945490178201599

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

7.550 × 10⁹⁶(97-digit number)

75501338700011124349…97865945490178201599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.550 × 10⁹⁶(97-digit number)

75501338700011124349…97865945490178201601

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

1.510 × 10⁹⁷(98-digit number)

15100267740002224869…95731890980356403199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.510 × 10⁹⁷(98-digit number)

15100267740002224869…95731890980356403201

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

3.020 × 10⁹⁷(98-digit number)

30200535480004449739…91463781960712806399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.020 × 10⁹⁷(98-digit number)

30200535480004449739…91463781960712806401

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

6.040 × 10⁹⁷(98-digit number)

60401070960008899479…82927563921425612799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.040 × 10⁹⁷(98-digit number)

60401070960008899479…82927563921425612801

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

1.208 × 10⁹⁸(99-digit number)

12080214192001779895…65855127842851225599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.208 × 10⁹⁸(99-digit number)

12080214192001779895…65855127842851225601

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

2.416 × 10⁹⁸(99-digit number)

24160428384003559791…31710255685702451199

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 #2,057,122

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