Block #1,469,875

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/24/2016, 12:08:33 AM · Difficulty 10.7418 · 5,347,077 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8fda448cf7bc18f8ea7615c97a00ec7b61670936b79450f0260dc70b05e19405

View on Chainz ↗

Height

#1,469,875

Difficulty

10.741775

Transactions

Size

937 B

Version

Bits

0abde4fb

Nonce

822,062,238

Timestamp

2/24/2016, 12:08:33 AM

Confirmations

5,347,077

Mined by

⛏️ P2SHARGdfq825GPL6HEpYpBTUuEVRoE3tJr4Gt

Merkle Root

94b4593462e640f86740b2ff484043f5e8f0fdea9a7987fa7ce3081479b590a5

Transactions (2)

Coinbase09cb18503597a2…58dbac41c4610c

1 in → 1 out8.6600 XPM110 B

ARGdfq82…E3tJr4Gt

b847409bb94b41…a080d82a89accf

1 in → 17 out80.9968 XPM736 B

AWEe7rAn…QxWNpYn6 AeVwC1gJ…5jcsgvkt AJo2SN3e…vJSgeTRb AYSS7wNK…KgMX99y4 ATH1rk2S…2U19MGCE

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.

3.079 × 10⁹⁶(97-digit number)

30795487987727623205…88480328009936732159

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

3.079 × 10⁹⁶(97-digit number)

30795487987727623205…88480328009936732159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.079 × 10⁹⁶(97-digit number)

30795487987727623205…88480328009936732161

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

6.159 × 10⁹⁶(97-digit number)

61590975975455246410…76960656019873464319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.159 × 10⁹⁶(97-digit number)

61590975975455246410…76960656019873464321

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

1.231 × 10⁹⁷(98-digit number)

12318195195091049282…53921312039746928639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.231 × 10⁹⁷(98-digit number)

12318195195091049282…53921312039746928641

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

2.463 × 10⁹⁷(98-digit number)

24636390390182098564…07842624079493857279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.463 × 10⁹⁷(98-digit number)

24636390390182098564…07842624079493857281

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

4.927 × 10⁹⁷(98-digit number)

49272780780364197128…15685248158987714559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.927 × 10⁹⁷(98-digit number)

49272780780364197128…15685248158987714561

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 #1,469,875

Cookie Preferences