Block #1,429,102

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/26/2016, 4:03:08 PM · Difficulty 10.7418 · 5,413,074 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e9baf0c637871981476937a2c13fbe0ec86f4ccbeef5950e76e7760a4f2c8f9c

View on Chainz ↗

Height

#1,429,102

Difficulty

10.741834

Transactions

Size

1.95 KB

Version

Bits

0abde8d4

Nonce

532,867,711

Timestamp

1/26/2016, 4:03:08 PM

Confirmations

5,413,074

Mined by

⛏️ P2SHAeMyPZPSc5VMwFUeJgVqrgs2Evzy8ydi4W

Merkle Root

9172d96e6c72ac48d1207b983be77737cb127fca9ba6f86586e2b4038a1eb967

Transactions (3)

Coinbased197d8bbd68ae6…a23fc29afb7946

1 in → 1 out8.6700 XPM109 B

AeMyPZPS…zy8ydi4W

8c95905fa0631e…26c44b9f94027d

5 in → 2 out40.5645 XPM818 B

AYWSNxZo…wMpmugUu AMUmnPLW…DkXcfLpC

b228c97d1401fb…79c1dc77f77234

1 in → 24 out198.1412 XPM975 B

AMfZuhaw…gFDWTRSN AUi1L7Uh…fWBAdCQZ Abpwfp3B…si9a6ff2 AHdzzGfy…qeVgWdje ATksCXD2…yrRDBzzA

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.

2.620 × 10⁹⁶(97-digit number)

26202041848177585353…88544665286210155519

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

2.620 × 10⁹⁶(97-digit number)

26202041848177585353…88544665286210155519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.620 × 10⁹⁶(97-digit number)

26202041848177585353…88544665286210155521

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

5.240 × 10⁹⁶(97-digit number)

52404083696355170707…77089330572420311039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.240 × 10⁹⁶(97-digit number)

52404083696355170707…77089330572420311041

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

1.048 × 10⁹⁷(98-digit number)

10480816739271034141…54178661144840622079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.048 × 10⁹⁷(98-digit number)

10480816739271034141…54178661144840622081

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

2.096 × 10⁹⁷(98-digit number)

20961633478542068282…08357322289681244159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.096 × 10⁹⁷(98-digit number)

20961633478542068282…08357322289681244161

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

4.192 × 10⁹⁷(98-digit number)

41923266957084136565…16714644579362488319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.192 × 10⁹⁷(98-digit number)

41923266957084136565…16714644579362488321

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

Block #1,429,102

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