Block #1,414,398

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 1/15/2016, 2:30:15 PM · Difficulty 10.7972 · 5,388,880 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f3435d6edada7822a030828b7858595ae24a089cb995343fcefa4522935b94ec

View on Chainz ↗

Height

#1,414,398

Difficulty

10.797172

Transactions

Size

13.38 KB

Version

Bits

0acc137e

Nonce

5,556,339

Timestamp

1/15/2016, 2:30:15 PM

Confirmations

5,388,880

Mined by

⛏️ P2SHAW9D9GpKQxvt5Tb9kSYt7cbi2rWZpCT1Fg

Merkle Root

d6ac076f39ccc6c69bae05ad7455af8fb00e01ae59245d0dfbad41a61167f5b7

Transactions (2)

Coinbase8961ab820aa5df…0aa85a5e286fe4

1 in → 1 out8.7000 XPM110 B

AW9D9GpK…WZpCT1Fg

0f51f2a610bfdd…bc62614b9a5253

91 in → 1 out29.5709 XPM13.18 KB

AKhwQDaD…RbcBi3U2

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.

1.078 × 10⁹⁶(97-digit number)

10787430801863865274…41582429829071819519

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

1.078 × 10⁹⁶(97-digit number)

10787430801863865274…41582429829071819519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.078 × 10⁹⁶(97-digit number)

10787430801863865274…41582429829071819521

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

2.157 × 10⁹⁶(97-digit number)

21574861603727730549…83164859658143639039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.157 × 10⁹⁶(97-digit number)

21574861603727730549…83164859658143639041

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

4.314 × 10⁹⁶(97-digit number)

43149723207455461098…66329719316287278079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.314 × 10⁹⁶(97-digit number)

43149723207455461098…66329719316287278081

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

8.629 × 10⁹⁶(97-digit number)

86299446414910922197…32659438632574556159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.629 × 10⁹⁶(97-digit number)

86299446414910922197…32659438632574556161

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

1.725 × 10⁹⁷(98-digit number)

17259889282982184439…65318877265149112319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.725 × 10⁹⁷(98-digit number)

17259889282982184439…65318877265149112321

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

3.451 × 10⁹⁷(98-digit number)

34519778565964368878…30637754530298224639

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