Block #1,469,256

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/23/2016, 10:16:03 AM · Difficulty 10.7525 · 5,357,047 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5ed1e212fbd23966aa7e9cd669698e358bf7400ae0f5484208c5811d981bc68b

View on Chainz ↗

Height

#1,469,256

Difficulty

10.752480

Transactions

Size

1.14 KB

Version

Bits

0ac0a28b

Nonce

796,429,861

Timestamp

2/23/2016, 10:16:03 AM

Confirmations

5,357,047

Mined by

⛏️ P2SHAcs21dcUVRbuVSPscGpBbeoc1tdNb1wFfs

Merkle Root

2bddbd71520abc98eabfd28cdec8ee2fec737103fbac9c5da30e444f51f12e69

Transactions (2)

Coinbasecc138348dff3b3…e3849c08caaaa6

1 in → 1 out8.6500 XPM110 B

Acs21dcU…dNb1wFfs

f1dc2707742879…7627251789a14c

6 in → 2 out2.2057 XPM969 B

AU7Zttam…nXo1qe1D Ab3TPdLf…zjgR2gJY

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.

2.862 × 10⁹²(93-digit number)

28624969384959505435…08619496809236223439

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

2.862 × 10⁹²(93-digit number)

28624969384959505435…08619496809236223439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.862 × 10⁹²(93-digit number)

28624969384959505435…08619496809236223441

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

5.724 × 10⁹²(93-digit number)

57249938769919010870…17238993618472446879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.724 × 10⁹²(93-digit number)

57249938769919010870…17238993618472446881

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

1.144 × 10⁹³(94-digit number)

11449987753983802174…34477987236944893759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.144 × 10⁹³(94-digit number)

11449987753983802174…34477987236944893761

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

2.289 × 10⁹³(94-digit number)

22899975507967604348…68955974473889787519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.289 × 10⁹³(94-digit number)

22899975507967604348…68955974473889787521

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

4.579 × 10⁹³(94-digit number)

45799951015935208696…37911948947779575039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.579 × 10⁹³(94-digit number)

45799951015935208696…37911948947779575041

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 #1,469,256

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