Block #416,774

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 2/23/2014, 4:02:52 PM · Difficulty 10.3996 · 6,400,021 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a8a6f39b345abaf8540233a4f5e3555ef3da071026ceb4765d8d8fe70a45a4fc

View on Chainz ↗

Height

#416,774

Difficulty

10.399641

Transactions

Size

392 B

Version

Bits

0a664ee6

Nonce

52,019

Timestamp

2/23/2014, 4:02:52 PM

Confirmations

6,400,021

Mined by

⛏️ P2SHAdGRRh1eP4JFvQMqy7y2pLsryDQmctLb24

Merkle Root

5c0c1a77dc80fb0cfd1fa0253a62a353c46a8b2400c74a0948d3a85234fdee80

Transactions (2)

Coinbase5664beca66ff81…1403f259a293ce

1 in → 2 out9.2400 XPM141 B

AdGRRh1e…QmctLb24 AKNbfPoc…jfkpwAyL

2cb32d19358020…e7b68d581c0b44

1 in → 1 out9.2000 XPM157 B

AYFCsYhj…NXHomGMr

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.

7.006 × 10¹⁰³(104-digit number)

70061590571590523464…40246265196595562879

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

7.006 × 10¹⁰³(104-digit number)

70061590571590523464…40246265196595562879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.006 × 10¹⁰³(104-digit number)

70061590571590523464…40246265196595562881

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

1.401 × 10¹⁰⁴(105-digit number)

14012318114318104692…80492530393191125759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.401 × 10¹⁰⁴(105-digit number)

14012318114318104692…80492530393191125761

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

2.802 × 10¹⁰⁴(105-digit number)

28024636228636209385…60985060786382251519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.802 × 10¹⁰⁴(105-digit number)

28024636228636209385…60985060786382251521

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

5.604 × 10¹⁰⁴(105-digit number)

56049272457272418771…21970121572764503039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.604 × 10¹⁰⁴(105-digit number)

56049272457272418771…21970121572764503041

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

1.120 × 10¹⁰⁵(106-digit number)

11209854491454483754…43940243145529006079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.120 × 10¹⁰⁵(106-digit number)

11209854491454483754…43940243145529006081

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

2.241 × 10¹⁰⁵(106-digit number)

22419708982908967508…87880486291058012159

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 #416,774

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