Block #1,649,397

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/28/2016, 7:03:30 PM · Difficulty 10.6524 · 5,166,659 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0ca0f5c68e3f371fc7952854709d7f73d44a025bb296824dc9dec5f63685e186

View on Chainz ↗

Height

#1,649,397

Difficulty

10.652405

Transactions

Size

8.80 KB

Version

Bits

0aa7040a

Nonce

552,702,912

Timestamp

6/28/2016, 7:03:30 PM

Confirmations

5,166,659

Mined by

⛏️ P2SHANemupP1zJS79fCLcmFD6XsGuWjv3bafHA

Merkle Root

573177cbd2db4316d5ce9793096e385fe7a2dc5673e986d05ff2fcc156702e3e

Transactions (2)

Coinbase4ebdb404a5302c…d01c8255bcc45f

1 in → 1 out8.9000 XPM109 B

ANemupP1…jv3bafHA

b232ee8410e127…0cc8ce16258682

59 in → 2 out110.3677 XPM8.61 KB

AXuGMgRg…siqDDkB7 AHNkwmbJ…EUxEmniY

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.

1.234 × 10⁹⁴(95-digit number)

12340961421165473212…25149657517447760639

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

1.234 × 10⁹⁴(95-digit number)

12340961421165473212…25149657517447760639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.234 × 10⁹⁴(95-digit number)

12340961421165473212…25149657517447760641

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

2.468 × 10⁹⁴(95-digit number)

24681922842330946424…50299315034895521279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.468 × 10⁹⁴(95-digit number)

24681922842330946424…50299315034895521281

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

4.936 × 10⁹⁴(95-digit number)

49363845684661892849…00598630069791042559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.936 × 10⁹⁴(95-digit number)

49363845684661892849…00598630069791042561

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

9.872 × 10⁹⁴(95-digit number)

98727691369323785698…01197260139582085119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.872 × 10⁹⁴(95-digit number)

98727691369323785698…01197260139582085121

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

1.974 × 10⁹⁵(96-digit number)

19745538273864757139…02394520279164170239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.974 × 10⁹⁵(96-digit number)

19745538273864757139…02394520279164170241

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 #1,649,397

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