Block #1,490,730

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/10/2016, 4:05:32 AM · Difficulty 10.6872 · 5,354,598 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f0ecfba4019496a11af6bcb883b6a2305336a96dced50cc7e2ddd597ecd02456

View on Chainz ↗

Height

#1,490,730

Difficulty

10.687233

Transactions

Size

1.35 KB

Version

Bits

0aafee86

Nonce

505,195,988

Timestamp

3/10/2016, 4:05:32 AM

Confirmations

5,354,598

Mined by

⛏️ P2SHATWwpc9oqMCuXQhdMqhJ65KzZo5NYdV3on

Merkle Root

1c10d39e8595fba5706c3825dd4b48dc2f6447356b5268a6ce22dfb085a043f8

Transactions (2)

Coinbaseca52f71fcae6d7…4479439a5c9aa7

1 in → 1 out8.7600 XPM109 B

ATWwpc9o…5NYdV3on

749e9df3a1b17d…af0877040bcb76

1 in → 30 out9.9002 XPM1.15 KB

AZxRQLuE…6zbgSr1a AR9FXwce…brYoUuX3 AS38oyda…fCzqRkvw AXpTeUvJ…cqytwrJz AUaaT32r…ZYAFbfPw

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.

5.440 × 10⁹⁶(97-digit number)

54408165698012858652…22964245806674196479

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

5.440 × 10⁹⁶(97-digit number)

54408165698012858652…22964245806674196479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.440 × 10⁹⁶(97-digit number)

54408165698012858652…22964245806674196481

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

1.088 × 10⁹⁷(98-digit number)

10881633139602571730…45928491613348392959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.088 × 10⁹⁷(98-digit number)

10881633139602571730…45928491613348392961

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

2.176 × 10⁹⁷(98-digit number)

21763266279205143461…91856983226696785919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.176 × 10⁹⁷(98-digit number)

21763266279205143461…91856983226696785921

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

4.352 × 10⁹⁷(98-digit number)

43526532558410286922…83713966453393571839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.352 × 10⁹⁷(98-digit number)

43526532558410286922…83713966453393571841

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

8.705 × 10⁹⁷(98-digit number)

87053065116820573844…67427932906787143679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.705 × 10⁹⁷(98-digit number)

87053065116820573844…67427932906787143681

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 #1,490,730

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