Block #2,135,407

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/28/2017, 4:55:07 AM · Difficulty 10.9012 · 4,704,000 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

495384067c84dea256d1e86bba66bcbb1b0d6ea2da115912a99be47c7ec335b4

View on Chainz ↗

Height

#2,135,407

Difficulty

10.901222

Transactions

Size

425 B

Version

Bits

0ae6b67d

Nonce

1,027,530,864

Timestamp

5/28/2017, 4:55:07 AM

Confirmations

4,704,000

Mined by

⛏️ P2SHAZCjzJqSrZbJ61YwNKRD3iGkNdn2r52WMG

Merkle Root

545de0b4f81ce727b7b0f9bfbadd14e97d912fbc63e8c3f119f79d7523fb5563

Transactions (2)

Coinbase53e32b6cbb0e40…995a4cd9e61c11

1 in → 1 out8.4100 XPM109 B

AZCjzJqS…n2r52WMG

e7a7d3ca1a1726…6bcacf8e2cd70c

1 in → 2 out12.1538 XPM225 B

AWSpM1vT…ukZRfqjD AWgScFW7…VeFBx8mu

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.

1.154 × 10⁹⁶(97-digit number)

11542884789815720522…03549147171663500799

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

1.154 × 10⁹⁶(97-digit number)

11542884789815720522…03549147171663500799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.154 × 10⁹⁶(97-digit number)

11542884789815720522…03549147171663500801

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

2.308 × 10⁹⁶(97-digit number)

23085769579631441045…07098294343327001599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.308 × 10⁹⁶(97-digit number)

23085769579631441045…07098294343327001601

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

4.617 × 10⁹⁶(97-digit number)

46171539159262882091…14196588686654003199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.617 × 10⁹⁶(97-digit number)

46171539159262882091…14196588686654003201

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

9.234 × 10⁹⁶(97-digit number)

92343078318525764182…28393177373308006399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.234 × 10⁹⁶(97-digit number)

92343078318525764182…28393177373308006401

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

1.846 × 10⁹⁷(98-digit number)

18468615663705152836…56786354746616012799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.846 × 10⁹⁷(98-digit number)

18468615663705152836…56786354746616012801

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

3.693 × 10⁹⁷(98-digit number)

36937231327410305673…13572709493232025599

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 #2,135,407

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