Block #1,513,402

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/26/2016, 6:03:00 PM · Difficulty 10.6035 · 5,302,690 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e3bb03cfdaa2eafaf7929b2e0a747695f16d28c46cdaaa29015651c81e50f849

View on Chainz ↗

Height

#1,513,402

Difficulty

10.603462

Transactions

Size

26.64 KB

Version

Bits

0a9a7c78

Nonce

449,788,543

Timestamp

3/26/2016, 6:03:00 PM

Confirmations

5,302,690

Mined by

⛏️ P2SHAMDZtb3sZ6LC1CxKYjUSjWBgjwYfUo4kAz

Merkle Root

5ce10cb52c7544e0b57ab8ad72f0c2836a3665df914a01abb2da0901f44b125c

Transactions (3)

Coinbase424cc00d305d6e…8b04e3f7801b65

1 in → 1 out9.3000 XPM109 B

AMDZtb3s…YfUo4kAz

fb6993b2aea83c…35f1c8497d514d

173 in → 1 out10.0000 XPM25.03 KB

AL7VCF7E…kwg84fNh

5b81bf402f2830…48ea2ec5ce46c9

1 in → 38 out79.3070 XPM1.42 KB

Ab4Nj6W1…sa413VZp AX6AtTQC…d6QrGxBB AJRpsnNi…HqGPsNv4 AevqxnfT…Nvf5VpW6 AQfsqCEf…KC9YtjHr

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.

6.067 × 10⁹⁴(95-digit number)

60670669695194384681…04505284570974187039

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

6.067 × 10⁹⁴(95-digit number)

60670669695194384681…04505284570974187039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.067 × 10⁹⁴(95-digit number)

60670669695194384681…04505284570974187041

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

1.213 × 10⁹⁵(96-digit number)

12134133939038876936…09010569141948374079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.213 × 10⁹⁵(96-digit number)

12134133939038876936…09010569141948374081

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

2.426 × 10⁹⁵(96-digit number)

24268267878077753872…18021138283896748159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.426 × 10⁹⁵(96-digit number)

24268267878077753872…18021138283896748161

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

4.853 × 10⁹⁵(96-digit number)

48536535756155507745…36042276567793496319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.853 × 10⁹⁵(96-digit number)

48536535756155507745…36042276567793496321

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

9.707 × 10⁹⁵(96-digit number)

97073071512311015490…72084553135586992639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.707 × 10⁹⁵(96-digit number)

97073071512311015490…72084553135586992641

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 #1,513,402

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