Block #415,932

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/23/2014, 2:08:13 AM · Difficulty 10.3980 · 6,387,280 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a056f7d84f756f05116031f520014cc9c75dca0589a6eb1360a3745b468c9df3

View on Chainz ↗

Height

#415,932

Difficulty

10.398042

Transactions

Size

2.12 KB

Version

Bits

0a65e617

Nonce

445

Timestamp

2/23/2014, 2:08:13 AM

Confirmations

6,387,280

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

edd53839a338ae02f153d092669ef042402c327e20a4bb8c0fca28c57b44bfe1

Transactions (4)

Coinbasedb1ae941cb6ab2…5b513c1b4dabd0

1 in → 1 out9.2700 XPM116 B

AbwWkWZt…kawDhufa

16ec0ae6df5366…c1a1c5e1b41a3b

2 in → 7 out18.3700 XPM476 B

AHm6vKLD…ybPBM5Sb APw1Mv6M…2733LDA1 AXDEZh15…FbrAPGkC AeKNrjNj…1NEq95Ta AZoyjqWo…cTWTRwva

3a4a772dad6c5a…6a032749e41fc2

8 in → 2 out2.3696 XPM1.23 KB

ANKfKtzn…yzEib2M5 AGUq89Fx…FmNyWa5c

58c08bc60a5740…4fee78b8f5e48c

1 in → 2 out3.0633 XPM227 B

ATiV5dCK…q2jDT9yR ALeXuaos…8qimwPHX

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.

3.206 × 10⁹⁶(97-digit number)

32063989697272772136…55506125687410206399

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

3.206 × 10⁹⁶(97-digit number)

32063989697272772136…55506125687410206399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.206 × 10⁹⁶(97-digit number)

32063989697272772136…55506125687410206401

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

6.412 × 10⁹⁶(97-digit number)

64127979394545544272…11012251374820412799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.412 × 10⁹⁶(97-digit number)

64127979394545544272…11012251374820412801

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

1.282 × 10⁹⁷(98-digit number)

12825595878909108854…22024502749640825599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.282 × 10⁹⁷(98-digit number)

12825595878909108854…22024502749640825601

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

2.565 × 10⁹⁷(98-digit number)

25651191757818217708…44049005499281651199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.565 × 10⁹⁷(98-digit number)

25651191757818217708…44049005499281651201

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

5.130 × 10⁹⁷(98-digit number)

51302383515636435417…88098010998563302399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.130 × 10⁹⁷(98-digit number)

51302383515636435417…88098010998563302401

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