Block #417,066

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/23/2014, 9:26:38 PM · Difficulty 10.3956 · 6,388,940 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3c390edfe26361bdfb74229e1d0b885fa2082729f71d538b829db300ed9a16aa

View on Chainz ↗

Height

#417,066

Difficulty

10.395646

Transactions

Size

1.52 KB

Version

Bits

0a654907

Nonce

7,834

Timestamp

2/23/2014, 9:26:38 PM

Confirmations

6,388,940

Mined by

AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

d0069bd4054af1724ec32181cf5e2c744bfee56e347820575ac854ddb36f6a7e

Transactions (2)

Coinbase43470df0ffa7c6…fa1ba7ae5224b5

1 in → 23 out9.2400 XPM845 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AYtDvcGs…VuAcA7m7 AGKhfQo2…h7fBXLX6 ALqxX1WA…hsKjbnXn

0401b6c939c92e…b9b32e695b2fd6

3 in → 7 out18.8466 XPM622 B

AJ4n9kZS…SnX6JMpQ AK6jxxMy…1dDKDr5h ALbMSCr6…Nv7gDkZj AbXWsrGo…29z6fjhy AG9LVB24…j5abSW7c

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.

1.176 × 10¹⁰⁰(101-digit number)

11761426162871925187…75680159756932910079

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

1.176 × 10¹⁰⁰(101-digit number)

11761426162871925187…75680159756932910079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.176 × 10¹⁰⁰(101-digit number)

11761426162871925187…75680159756932910081

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

2.352 × 10¹⁰⁰(101-digit number)

23522852325743850375…51360319513865820159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.352 × 10¹⁰⁰(101-digit number)

23522852325743850375…51360319513865820161

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

4.704 × 10¹⁰⁰(101-digit number)

47045704651487700751…02720639027731640319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.704 × 10¹⁰⁰(101-digit number)

47045704651487700751…02720639027731640321

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

9.409 × 10¹⁰⁰(101-digit number)

94091409302975401503…05441278055463280639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.409 × 10¹⁰⁰(101-digit number)

94091409302975401503…05441278055463280641

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

1.881 × 10¹⁰¹(102-digit number)

18818281860595080300…10882556110926561279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.881 × 10¹⁰¹(102-digit number)

18818281860595080300…10882556110926561281

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