Block #417,126

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 2/23/2014, 10:23:55 PM · Difficulty 10.3959 · 6,389,502 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0d93941c3c4f89f75ef0b9896cb97d532cefa45f7a28f18bde7fd29f8b15da77

View on Chainz ↗

Height

#417,126

Difficulty

10.395950

Transactions

Size

969 B

Version

Bits

0a655cf8

Nonce

3,969

Timestamp

2/23/2014, 10:23:55 PM

Confirmations

6,389,502

Mined by

⛏️ fAac9Hjdgnw4T4L2csqLecJsmZjP4ktypc3

Merkle Root

e763714b3ea40fb5c34892e855e3a19313244980aace61a801297a26fc670dc3

Transactions (1)

Coinbasee763714b3ea40f…297a26fc670dc3

1 in → 24 out9.2344 XPM879 B

Aac9Hjdg…P4ktypc3 AGKhfQo2…h7fBXLX6 ALqxX1WA…hsKjbnXn AUAhhM4J…os8UBUGE ARSeozDw…C9HtARnj

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.

8.340 × 10⁹³(94-digit number)

83406079989456043191…22117941480480871899

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

8.340 × 10⁹³(94-digit number)

83406079989456043191…22117941480480871899

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.340 × 10⁹³(94-digit number)

83406079989456043191…22117941480480871901

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

1.668 × 10⁹⁴(95-digit number)

16681215997891208638…44235882960961743799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.668 × 10⁹⁴(95-digit number)

16681215997891208638…44235882960961743801

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

3.336 × 10⁹⁴(95-digit number)

33362431995782417276…88471765921923487599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.336 × 10⁹⁴(95-digit number)

33362431995782417276…88471765921923487601

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

6.672 × 10⁹⁴(95-digit number)

66724863991564834552…76943531843846975199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.672 × 10⁹⁴(95-digit number)

66724863991564834552…76943531843846975201

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

1.334 × 10⁹⁵(96-digit number)

13344972798312966910…53887063687693950399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.334 × 10⁹⁵(96-digit number)

13344972798312966910…53887063687693950401

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

2.668 × 10⁹⁵(96-digit number)

26689945596625933821…07774127375387900799

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #417,126

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