Block #1,989,239

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 2/18/2017, 11:58:29 PM · Difficulty 10.7362 · 4,852,828 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

98bfcc68250f08359749c711ac048cd36db8e891701cc47143c78083116c3e4a

View on Chainz ↗

Height

#1,989,239

Difficulty

10.736215

Transactions

Size

2.73 KB

Version

Bits

0abc789b

Nonce

67,245,795

Timestamp

2/18/2017, 11:58:29 PM

Confirmations

4,852,828

Mined by

⛏️ P2SHAZZxxPnsmRysrgTuhDBwBwqJLgf5QAEzdh

Merkle Root

9fbaf3370f58caaec98358a8a78099c1aa57161e870c59366422c45ca666a777

Transactions (2)

Coinbase16bd9b5b401a80…f7e1ad1b78ed13

1 in → 1 out8.6900 XPM110 B

AZZxxPns…f5QAEzdh

67b4ebfa8a361c…86c8e10d81499e

17 in → 2 out1137.4412 XPM2.54 KB

AZ7xo3ni…aXTAFhZR AdKh1Apd…vWnFMSBy

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.

6.715 × 10⁹⁴(95-digit number)

67151850662772353857…02959833457077615839

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

6.715 × 10⁹⁴(95-digit number)

67151850662772353857…02959833457077615839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.715 × 10⁹⁴(95-digit number)

67151850662772353857…02959833457077615841

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

1.343 × 10⁹⁵(96-digit number)

13430370132554470771…05919666914155231679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.343 × 10⁹⁵(96-digit number)

13430370132554470771…05919666914155231681

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

2.686 × 10⁹⁵(96-digit number)

26860740265108941542…11839333828310463359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.686 × 10⁹⁵(96-digit number)

26860740265108941542…11839333828310463361

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

5.372 × 10⁹⁵(96-digit number)

53721480530217883085…23678667656620926719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.372 × 10⁹⁵(96-digit number)

53721480530217883085…23678667656620926721

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

1.074 × 10⁹⁶(97-digit number)

10744296106043576617…47357335313241853439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.074 × 10⁹⁶(97-digit number)

10744296106043576617…47357335313241853441

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

2.148 × 10⁹⁶(97-digit number)

21488592212087153234…94714670626483706879

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 #1,989,239

Cookie Preferences