Block #1,626,557

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/13/2016, 12:36:27 PM · Difficulty 10.5869 · 5,179,551 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

bdbc47bf22a35f8714035707610f12ccba02619043a6965275e9386a78c91d47

View on Chainz ↗

Height

#1,626,557

Difficulty

10.586919

Transactions

Size

5.74 KB

Version

Bits

0a964056

Nonce

8,469,374

Timestamp

6/13/2016, 12:36:27 PM

Confirmations

5,179,551

Mined by

⛏️ P2SHAHW9FsP2uGnvCpZ1sbg5tZ6tDd8isnQFgB

Merkle Root

86ebd22970603870f8f66946ce1289b9fcccda9c63fd4f5c9dd62e09ef8ca616

Transactions (4)

Coinbase37c4583f298011…e53f4924534e8c

1 in → 1 out8.9700 XPM109 B

AHW9FsP2…8isnQFgB

d1f1be3be9949d…393ef5854cfd18

1 in → 51 out29.1102 XPM1.85 KB

AeRufDFD…yftHXdHD AXHDhdvA…ZuSoMvKz AMomWVZx…cp2KvBDi AQ3JL4pf…yLvrivvq AQQayUTp…oYZtRgqn

7a162d2e977b67…413a94d24884f7

1 in → 51 out6.6264 XPM1.85 KB

AbUMzijX…TmVncjz5 AdcQgjQa…s7MkkLNB AMnA18Q4…3xWVnACm ALDXt9Po…vPJp9J6Z AaAK8CY6…23wmsA2Z

3aa0f02711a8d7…0892957a6b3760

1 in → 51 out9.9800 XPM1.85 KB

AdyeCMS5…ssfimQDf AT2hZpt5…ygN5oMvw AZN3ZN8C…X6m3Fwnk AeTCoaWY…PWJdDTxk ASj5BRL7…pfqKMfMi

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.

2.017 × 10⁹⁷(98-digit number)

20177978922767466904…76103458944687800319

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

2.017 × 10⁹⁷(98-digit number)

20177978922767466904…76103458944687800319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.017 × 10⁹⁷(98-digit number)

20177978922767466904…76103458944687800321

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

4.035 × 10⁹⁷(98-digit number)

40355957845534933809…52206917889375600639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.035 × 10⁹⁷(98-digit number)

40355957845534933809…52206917889375600641

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

8.071 × 10⁹⁷(98-digit number)

80711915691069867618…04413835778751201279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.071 × 10⁹⁷(98-digit number)

80711915691069867618…04413835778751201281

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

1.614 × 10⁹⁸(99-digit number)

16142383138213973523…08827671557502402559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.614 × 10⁹⁸(99-digit number)

16142383138213973523…08827671557502402561

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

3.228 × 10⁹⁸(99-digit number)

32284766276427947047…17655343115004805119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.228 × 10⁹⁸(99-digit number)

32284766276427947047…17655343115004805121

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