Block #1,465,934

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/20/2016, 6:04:23 PM · Difficulty 10.7770 · 5,359,725 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

401e5c24305f05ccd4c8f6a0bacda69f7bb88e374e930daecf65c8a42358da45

View on Chainz ↗

Height

#1,465,934

Difficulty

10.777033

Transactions

Size

1.25 KB

Version

Bits

0ac6eba5

Nonce

1,899,949,977

Timestamp

2/20/2016, 6:04:23 PM

Confirmations

5,359,725

Mined by

⛏️ P2SHAT5fk2kpT54uw7uxTnN6vV2ofMEhKLAGLj

Merkle Root

dc8087925ac770b13c7e5dc6cfb68414eef5e325f0b96ba457f9abe1b379dd3e

Transactions (2)

Coinbase2a638adbf7bb52…7761cfa2d4e422

1 in → 1 out8.6200 XPM109 B

AT5fk2kp…EhKLAGLj

cfbb62026618ca…c630a05c181276

1 in → 27 out140.0581 XPM1.05 KB

AdCUmxeB…e2r7uEas AHnn9vxL…nswpLCDL ALdzBuZj…qhNaLqze ASaabTJm…T52GVhot ARW3axQ3…u1GC9Kds

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.

4.035 × 10⁹⁵(96-digit number)

40359390103651060653…11083080137238271999

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

4.035 × 10⁹⁵(96-digit number)

40359390103651060653…11083080137238271999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.035 × 10⁹⁵(96-digit number)

40359390103651060653…11083080137238272001

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

8.071 × 10⁹⁵(96-digit number)

80718780207302121306…22166160274476543999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.071 × 10⁹⁵(96-digit number)

80718780207302121306…22166160274476544001

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

1.614 × 10⁹⁶(97-digit number)

16143756041460424261…44332320548953087999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.614 × 10⁹⁶(97-digit number)

16143756041460424261…44332320548953088001

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

3.228 × 10⁹⁶(97-digit number)

32287512082920848522…88664641097906175999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.228 × 10⁹⁶(97-digit number)

32287512082920848522…88664641097906176001

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

6.457 × 10⁹⁶(97-digit number)

64575024165841697045…77329282195812351999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.457 × 10⁹⁶(97-digit number)

64575024165841697045…77329282195812352001

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 #1,465,934

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