Block #2,150,605

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 6/7/2017, 8:26:20 PM · Difficulty 10.8990 · 4,675,643 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

87c965bb6ac062a775a2b88646c1e22baecf34e261168ade120b3903336fd12f

View on Chainz ↗

Height

#2,150,605

Difficulty

10.898992

Transactions

Size

3.02 KB

Version

Bits

0ae62455

Nonce

582,730,229

Timestamp

6/7/2017, 8:26:20 PM

Confirmations

4,675,643

Mined by

⛏️ P2SHAPfxhinacvw4t1cnaNhVLstm6B1LjyVkz4

Merkle Root

d1a01659e9662239c623690709bba6d8a74801621c3f962a8caf97ca8edccaf3

Transactions (2)

Coinbase352077ab63f50b…14fe109197c104

1 in → 1 out8.4300 XPM110 B

APfxhina…1LjyVkz4

466a7b089190b0…999d4ca8588daa

19 in → 2 out169.0010 XPM2.82 KB

AYq1G1AX…5JZtNa9G AccDYhvZ…Svw8n2Hf

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.

6.526 × 10⁹⁸(99-digit number)

65268975441548205839…97688658086438830079

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

6.526 × 10⁹⁸(99-digit number)

65268975441548205839…97688658086438830079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.526 × 10⁹⁸(99-digit number)

65268975441548205839…97688658086438830081

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

1.305 × 10⁹⁹(100-digit number)

13053795088309641167…95377316172877660159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.305 × 10⁹⁹(100-digit number)

13053795088309641167…95377316172877660161

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

2.610 × 10⁹⁹(100-digit number)

26107590176619282335…90754632345755320319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.610 × 10⁹⁹(100-digit number)

26107590176619282335…90754632345755320321

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

5.221 × 10⁹⁹(100-digit number)

52215180353238564671…81509264691510640639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.221 × 10⁹⁹(100-digit number)

52215180353238564671…81509264691510640641

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

1.044 × 10¹⁰⁰(101-digit number)

10443036070647712934…63018529383021281279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.044 × 10¹⁰⁰(101-digit number)

10443036070647712934…63018529383021281281

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

2.088 × 10¹⁰⁰(101-digit number)

20886072141295425868…26037058766042562559

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 #2,150,605

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