Block #1,015,632

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 4/14/2015, 9:27:37 AM · Difficulty 10.7277 · 5,797,111 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7882e62f813f7d727309b2dae3f92787e388ae2426279952259cf3589cb24c09

View on Chainz ↗

Height

#1,015,632

Difficulty

10.727662

Transactions

Size

1.00 KB

Version

Bits

0aba4809

Nonce

325,690,538

Timestamp

4/14/2015, 9:27:37 AM

Confirmations

5,797,111

Mined by

⛏️ P2SHAb6WageJmQ1y4te8Tcf9EuSqJCV6ENDRQX

Merkle Root

8e78965c1b6e76a1c5bad482deac8f086fefb5d19561e1e9abf325dd90841f89

Transactions (4)

Coinbase18a35752c9b593…bf35228afc73f6

1 in → 1 out8.7100 XPM109 B

Ab6WageJ…V6ENDRQX

b13ec2e37a43cb…595c23221523b3

2 in → 2 out15.9364 XPM374 B

AKytiV1V…6PAC4cVw ASEV2tcM…wUNfB6WE

1d77a97679756c…3a0f08dfdbb39e

1 in → 2 out7.4419 XPM226 B

Acjx2FrY…cz2DsAEo AKKnFqop…xxu5XWDy

98419349c327e0…4649208b3490c8

1 in → 2 out3.8807 XPM225 B

Ae7YXEyn…hnSYZsCr APuisWfU…okcdHyxA

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.

4.171 × 10⁹⁷(98-digit number)

41715734879920175280…65072921139759513599

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

4.171 × 10⁹⁷(98-digit number)

41715734879920175280…65072921139759513599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.171 × 10⁹⁷(98-digit number)

41715734879920175280…65072921139759513601

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

8.343 × 10⁹⁷(98-digit number)

83431469759840350560…30145842279519027199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.343 × 10⁹⁷(98-digit number)

83431469759840350560…30145842279519027201

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

1.668 × 10⁹⁸(99-digit number)

16686293951968070112…60291684559038054399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.668 × 10⁹⁸(99-digit number)

16686293951968070112…60291684559038054401

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

3.337 × 10⁹⁸(99-digit number)

33372587903936140224…20583369118076108799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.337 × 10⁹⁸(99-digit number)

33372587903936140224…20583369118076108801

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

6.674 × 10⁹⁸(99-digit number)

66745175807872280448…41166738236152217599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.674 × 10⁹⁸(99-digit number)

66745175807872280448…41166738236152217601

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

1.334 × 10⁹⁹(100-digit number)

13349035161574456089…82333476472304435199

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 #1,015,632

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