Block #1,303,920

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/29/2015, 4:03:51 PM · Difficulty 10.8533 · 5,504,422 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6f9beb03d5bc2fff3024efc440c93501de63bfc3006521fb415ca582875a2a4e

View on Chainz ↗

Height

#1,303,920

Difficulty

10.853350

Transactions

Size

1.31 KB

Version

Bits

0ada7521

Nonce

246,314,207

Timestamp

10/29/2015, 4:03:51 PM

Confirmations

5,504,422

Mined by

⛏️ P2SHAHSASs4cPigUgdxnsNc4dmQxtmKHs5gFQq

Merkle Root

8eb8e34ca7cb20ca74a6b70c049a00765aa01d89def01f49617a45b68f95d029

Transactions (2)

Coinbaseb38f1c855a9858…b629a76ff87e01

1 in → 1 out8.5000 XPM110 B

AHSASs4c…KHs5gFQq

c6b851a287de88…276987ff9e6aae

1 in → 29 out66.5655 XPM1.12 KB

AVXvAefY…XZMwJD1n AKEyxA4X…rZEnR7kp AXnP6PCK…hbBwJiAA AVQCLFbe…WMFoj6Jg ATnyfWYP…agt1aJCp

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.

5.673 × 10⁹⁶(97-digit number)

56738337294808029150…56328071462594129919

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

5.673 × 10⁹⁶(97-digit number)

56738337294808029150…56328071462594129919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.673 × 10⁹⁶(97-digit number)

56738337294808029150…56328071462594129921

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

1.134 × 10⁹⁷(98-digit number)

11347667458961605830…12656142925188259839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.134 × 10⁹⁷(98-digit number)

11347667458961605830…12656142925188259841

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

2.269 × 10⁹⁷(98-digit number)

22695334917923211660…25312285850376519679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.269 × 10⁹⁷(98-digit number)

22695334917923211660…25312285850376519681

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

4.539 × 10⁹⁷(98-digit number)

45390669835846423320…50624571700753039359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.539 × 10⁹⁷(98-digit number)

45390669835846423320…50624571700753039361

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

9.078 × 10⁹⁷(98-digit number)

90781339671692846641…01249143401506078719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.078 × 10⁹⁷(98-digit number)

90781339671692846641…01249143401506078721

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 #1,303,920

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