Block #1,627,187

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/13/2016, 10:33:49 PM · Difficulty 10.5896 · 5,179,027 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

021e338bf4ee2a43b32ebefcffc1fbc020f0853bfa982e8d93ec7e3a254f0d49

View on Chainz ↗

Height

#1,627,187

Difficulty

10.589551

Transactions

Size

6.17 KB

Version

Bits

0a96ecd8

Nonce

1,421,668,942

Timestamp

6/13/2016, 10:33:49 PM

Confirmations

5,179,027

Mined by

⛏️ P2SHAHkWSyg8dhpiZSUH6tVGMbFkqoH19wDcLz

Merkle Root

bdb4b9a78350579fbecfa01b7c35b3d225a1c0bda20e0d981d14489893675dec

Transactions (4)

Coinbasea8106c716f70c6…ae65df8f3de6c9

1 in → 1 out8.9700 XPM109 B

AHkWSyg8…H19wDcLz

114c8a87c2cdbc…b850d331d41439

1 in → 51 out4.6278 XPM1.85 KB

APs87Vmm…WcE7mKvk AHMtP94K…UJnjvqYh AKNEReZh…z67yMmw4 ANrR73i5…pdfP9FeT AQ3JL4pf…yLvrivvq

c2b34a4a5cc0a8…d4e2c7a84a3ebc

4 in → 51 out11.5742 XPM2.28 KB

AKUZ2tr9…Hct29YhT APNk7qaT…TdakVrNi AHEx2Jho…RRM42dJY Af4W9WTo…ixQmMk1J AMiZyJ5m…RED5XPBR

28c8bd1ea42bc7…1e8946af5b5775

1 in → 51 out1.6873 XPM1.85 KB

AQXDvXUU…vcLxjupK AQ8wzrGp…Fuq2sFPi ASg1fR7F…b5f5CVKW AZ2Dv6vs…YoKVyFme AVkhd4sr…uuK532n9

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.

3.216 × 10⁹⁶(97-digit number)

32165011039619974420…40023233752323962879

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

3.216 × 10⁹⁶(97-digit number)

32165011039619974420…40023233752323962879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.216 × 10⁹⁶(97-digit number)

32165011039619974420…40023233752323962881

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

6.433 × 10⁹⁶(97-digit number)

64330022079239948841…80046467504647925759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.433 × 10⁹⁶(97-digit number)

64330022079239948841…80046467504647925761

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

1.286 × 10⁹⁷(98-digit number)

12866004415847989768…60092935009295851519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.286 × 10⁹⁷(98-digit number)

12866004415847989768…60092935009295851521

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

2.573 × 10⁹⁷(98-digit number)

25732008831695979536…20185870018591703039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.573 × 10⁹⁷(98-digit number)

25732008831695979536…20185870018591703041

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

5.146 × 10⁹⁷(98-digit number)

51464017663391959073…40371740037183406079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.146 × 10⁹⁷(98-digit number)

51464017663391959073…40371740037183406081

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