Block #2,125,364

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/20/2017, 12:58:12 PM · Difficulty 10.9186 · 4,708,173 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

bff82e152fb3dff328ac010fa0f248c7aaa25bd01a60bcd682b3519db68310c0

View on Chainz ↗

Height

#2,125,364

Difficulty

10.918621

Transactions

Size

720 B

Version

Bits

0aeb2aba

Nonce

157,398,031

Timestamp

5/20/2017, 12:58:12 PM

Confirmations

4,708,173

Mined by

⛏️ P2SHAH8bYPxvBYo9nkAxDEb5Rw7sVShugGtWKn

Merkle Root

ca2790cd2180c0e1acfde27517086ef935edfb715a0329dc58eabdc9885a79a0

Transactions (2)

Coinbased29a09d3862a3e…35eb183a83132a

1 in → 1 out8.3800 XPM110 B

AH8bYPxv…hugGtWKn

82e211e07d2a05…aad9438a4a6368

3 in → 2 out0.1145 XPM520 B

AbvhK1fr…EWcHDzqx ATigvLyp…cXGh9ytM

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.

4.673 × 10⁹³(94-digit number)

46730461317904926478…78761869343930024619

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

4.673 × 10⁹³(94-digit number)

46730461317904926478…78761869343930024619

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.673 × 10⁹³(94-digit number)

46730461317904926478…78761869343930024621

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

9.346 × 10⁹³(94-digit number)

93460922635809852957…57523738687860049239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.346 × 10⁹³(94-digit number)

93460922635809852957…57523738687860049241

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

1.869 × 10⁹⁴(95-digit number)

18692184527161970591…15047477375720098479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.869 × 10⁹⁴(95-digit number)

18692184527161970591…15047477375720098481

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

3.738 × 10⁹⁴(95-digit number)

37384369054323941182…30094954751440196959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.738 × 10⁹⁴(95-digit number)

37384369054323941182…30094954751440196961

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

7.476 × 10⁹⁴(95-digit number)

74768738108647882365…60189909502880393919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.476 × 10⁹⁴(95-digit number)

74768738108647882365…60189909502880393921

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 #2,125,364

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