Block #1,597,206

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/23/2016, 10:05:15 PM · Difficulty 10.6112 · 5,245,097 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

95dc4f5283cab1499645c2ae9a4c73ea605d3f770d6e7a4dc9f9d8fc77e7c401

View on Chainz ↗

Height

#1,597,206

Difficulty

10.611239

Transactions

Size

1.21 KB

Version

Bits

0a9c7a27

Nonce

888,602,121

Timestamp

5/23/2016, 10:05:15 PM

Confirmations

5,245,097

Mined by

⛏️ P2SHAdSkTpXUzkyxtntxnL323cCmkDP51QCQZd

Merkle Root

6154f65369dc233d9b31be43296bca033e54b8499f628c6c4f17bdb33ba92fd8

Transactions (2)

Coinbase7b4cd78ed6048d…4c6e3d1a9949ba

1 in → 1 out8.8900 XPM110 B

AdSkTpXU…P51QCQZd

2177ab4bf2689d…d646643493ddcc

1 in → 26 out27.4428 XPM1.02 KB

AVmknThE…WizW7din ALQG96NK…5zPi39NB AZYDDdZm…pCLumG1j ASwncKHm…gjcC3Skf AQE3teJ3…nB8XvZYo

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.

3.824 × 10⁹⁴(95-digit number)

38245248694021609550…59546461053852902399

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

3.824 × 10⁹⁴(95-digit number)

38245248694021609550…59546461053852902399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.824 × 10⁹⁴(95-digit number)

38245248694021609550…59546461053852902401

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

7.649 × 10⁹⁴(95-digit number)

76490497388043219100…19092922107705804799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.649 × 10⁹⁴(95-digit number)

76490497388043219100…19092922107705804801

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

1.529 × 10⁹⁵(96-digit number)

15298099477608643820…38185844215411609599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.529 × 10⁹⁵(96-digit number)

15298099477608643820…38185844215411609601

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

3.059 × 10⁹⁵(96-digit number)

30596198955217287640…76371688430823219199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.059 × 10⁹⁵(96-digit number)

30596198955217287640…76371688430823219201

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

6.119 × 10⁹⁵(96-digit number)

61192397910434575280…52743376861646438399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.119 × 10⁹⁵(96-digit number)

61192397910434575280…52743376861646438401

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 #1,597,206

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