Block #1,481,974

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/3/2016, 3:07:43 PM · Difficulty 10.7256 · 5,351,823 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a3e03ec04bfa7ab4f4a5154348ea938d0f6a714d4a7284d5485fc5a03d1fbc29

View on Chainz ↗

Height

#1,481,974

Difficulty

10.725578

Transactions

Size

1.60 KB

Version

Bits

0ab9bf83

Nonce

52,239,764

Timestamp

3/3/2016, 3:07:43 PM

Confirmations

5,351,823

Mined by

⛏️ P2SHAPxAa5LrXz4rUVvvvFUL7sDhaDjBmQPkVx

Merkle Root

7ba7b2261f7321b3e549a56d47f931eb6be0b770ab2f6109f86947ff37406515

Transactions (3)

Coinbase3a36cb62d1f3c1…0ae6867472f26b

1 in → 1 out8.7100 XPM110 B

APxAa5Lr…jBmQPkVx

65e43a081d8e7a…8dc67514b1a595

1 in → 2 out0.3557 XPM225 B

ATZuEKEX…qjL4mRxL AbVDkkFS…Qvw4PG7w

f316fa99f1e483…83ea0a84b6c954

1 in → 31 out151.9879 XPM1.18 KB

AdyPbdgH…yv3sg2su AXbqV9PY…Vo2Ekhd4 AZBE8zdv…wKnLvfaW AahNe9Eb…j7WvUkU7 AWz1KjjL…8TzR4rmg

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.

3.704 × 10⁹⁵(96-digit number)

37048634859636185235…28718230925982071999

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

3.704 × 10⁹⁵(96-digit number)

37048634859636185235…28718230925982071999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.704 × 10⁹⁵(96-digit number)

37048634859636185235…28718230925982072001

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

7.409 × 10⁹⁵(96-digit number)

74097269719272370471…57436461851964143999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.409 × 10⁹⁵(96-digit number)

74097269719272370471…57436461851964144001

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

1.481 × 10⁹⁶(97-digit number)

14819453943854474094…14872923703928287999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.481 × 10⁹⁶(97-digit number)

14819453943854474094…14872923703928288001

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

2.963 × 10⁹⁶(97-digit number)

29638907887708948188…29745847407856575999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.963 × 10⁹⁶(97-digit number)

29638907887708948188…29745847407856576001

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

5.927 × 10⁹⁶(97-digit number)

59277815775417896377…59491694815713151999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.927 × 10⁹⁶(97-digit number)

59277815775417896377…59491694815713152001

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 #1,481,974

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