Block #416,846

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/23/2014, 5:14:07 PM · Difficulty 10.3996 · 6,400,639 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

cbb37f899ac97370dd2e9836603721e4ac3495a30e7b726194892222c2a4d88b

View on Chainz ↗

Height

#416,846

Difficulty

10.399567

Transactions

Size

1.64 KB

Version

Bits

0a664a05

Nonce

253,040

Timestamp

2/23/2014, 5:14:07 PM

Confirmations

6,400,639

Mined by

⛏️ N\aSAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

9ee8cb745ab2200edf96eb60e8d6ed64e1a982c7aa28205837698613356f877b

Transactions (4)

Coinbasea188dcbf278f69…471f523e33d98e

1 in → 25 out9.2300 XPM913 B

AQvZBsUo…hppgRZTJ ATKK7iFz…wZm46KN1 AGKhfQo2…h7fBXLX6 AZV4TwxQ…8JnQqSoH AQwRN8bE…V8PsTcY9

f05aa9780396f7…9aebc707c51d17

1 in → 2 out5.1443 XPM225 B

ALHZ9dUz…AwA2AAvf ALPV199F…QuvZZ3xm

faa7ee4de045ce…311b6026c18a8e

1 in → 2 out5.1253 XPM226 B

AatdaVa3…N23bwCXM ASnqRoSP…Mm4FhFM5

f39a3c0901052d…3789b9a1781507

1 in → 2 out1.0252 XPM226 B

AcLTqept…19s1L74t AMiVTMtt…4Knq1ve9

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.

2.026 × 10⁹⁵(96-digit number)

20261123151286572160…38355038793984189399

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

2.026 × 10⁹⁵(96-digit number)

20261123151286572160…38355038793984189399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.026 × 10⁹⁵(96-digit number)

20261123151286572160…38355038793984189401

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

4.052 × 10⁹⁵(96-digit number)

40522246302573144320…76710077587968378799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.052 × 10⁹⁵(96-digit number)

40522246302573144320…76710077587968378801

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

8.104 × 10⁹⁵(96-digit number)

81044492605146288641…53420155175936757599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.104 × 10⁹⁵(96-digit number)

81044492605146288641…53420155175936757601

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

1.620 × 10⁹⁶(97-digit number)

16208898521029257728…06840310351873515199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.620 × 10⁹⁶(97-digit number)

16208898521029257728…06840310351873515201

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

3.241 × 10⁹⁶(97-digit number)

32417797042058515456…13680620703747030399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.241 × 10⁹⁶(97-digit number)

32417797042058515456…13680620703747030401

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 #416,846

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