Block #2,177,918

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 6/25/2017, 7:52:22 PM · Difficulty 10.9246 · 4,652,574 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

48d0e77b243e26b182b57daf5db0e91768934420a027d8ccd6a3f2e5d6121d06

View on Chainz ↗

Height

#2,177,918

Difficulty

10.924573

Transactions

Size

877 B

Version

Bits

0aecb0d1

Nonce

1,086,023,443

Timestamp

6/25/2017, 7:52:22 PM

Confirmations

4,652,574

Mined by

⛏️ P2SHAWvijvjVNxMXz6FLzvRuTiGyHbPGh4Mh5d

Merkle Root

6a635b6240ae2d02fedc603e78702e260cec338874c97856471b031b4b184d6c

Transactions (4)

Coinbase2d1cefe09963c6…5fe242045e20e3

1 in → 1 out8.4000 XPM109 B

AWvijvjV…PGh4Mh5d

4f5c6e3999ce4d…86aa41d19692de

1 in → 2 out163904.8261 XPM226 B

ASmZerQn…C6tmfN6Z AUU5CooP…9tBwKBPC

594e4db7805ee6…8e39390458bcb2

1 in → 2 out99999.9900 XPM225 B

ALfDGB68…kxcTkU6B AbvEZv3o…PLodVQND

21d4915799189b…19688c139ac451

1 in → 2 out99061.6448 XPM226 B

AQMaJjtt…YyG7d84s AXJirPRv…CWeHX8r8

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.

1.018 × 10⁹⁷(98-digit number)

10181923546548748452…45701186799075123199

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

1.018 × 10⁹⁷(98-digit number)

10181923546548748452…45701186799075123199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.018 × 10⁹⁷(98-digit number)

10181923546548748452…45701186799075123201

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

2.036 × 10⁹⁷(98-digit number)

20363847093097496904…91402373598150246399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.036 × 10⁹⁷(98-digit number)

20363847093097496904…91402373598150246401

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

4.072 × 10⁹⁷(98-digit number)

40727694186194993808…82804747196300492799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.072 × 10⁹⁷(98-digit number)

40727694186194993808…82804747196300492801

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

8.145 × 10⁹⁷(98-digit number)

81455388372389987616…65609494392600985599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.145 × 10⁹⁷(98-digit number)

81455388372389987616…65609494392600985601

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

1.629 × 10⁹⁸(99-digit number)

16291077674477997523…31218988785201971199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.629 × 10⁹⁸(99-digit number)

16291077674477997523…31218988785201971201

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

3.258 × 10⁹⁸(99-digit number)

32582155348955995046…62437977570403942399

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 #2,177,918

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