Block #417,658

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/24/2014, 7:45:46 AM · Difficulty 10.3927 · 6,388,445 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

92d42ee249a92f0fccf0e3e7ea7e39819bb19f3130ed23a8136fac3d5097c3ed

View on Chainz ↗

Height

#417,658

Difficulty

10.392730

Transactions

Size

1.48 KB

Version

Bits

0a6489f2

Nonce

43,728

Timestamp

2/24/2014, 7:45:46 AM

Confirmations

6,388,445

Mined by

⛏️ z_nAMVf7JrgD9LEuSS2R27DgQAdb3xd5AVR7C

Merkle Root

078d5be06f781d9fce2cacc4f90fba9a937db92373a71aeeadcd418743f00d76

Transactions (3)

Coinbasee0acea97353a34…cce4baa2ce5c8a

1 in → 2 out9.2600 XPM131 B

AMVf7Jrg…xd5AVR7C AJno7LX2…vo4wdWtY

451ad615ab7da2…cada5bac1a7c82

3 in → 7 out18.8332 XPM625 B

AeKNrjNj…1NEq95Ta AZYdGfZ7…q5ScxP7b AScbVWdz…cLMKqFjL AXWdmUfv…DmgM1U8i ALrZxq5u…jReX3z9e

0124e6ed11257b…a9e544fda99fe3

4 in → 2 out1.0170 XPM669 B

Ab5iAXgM…NWEj45eQ ASTjqyiR…Lkb6FcHY

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.

5.315 × 10⁹⁹(100-digit number)

53157454415946316076…89416638459630709439

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

5.315 × 10⁹⁹(100-digit number)

53157454415946316076…89416638459630709439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.315 × 10⁹⁹(100-digit number)

53157454415946316076…89416638459630709441

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

1.063 × 10¹⁰⁰(101-digit number)

10631490883189263215…78833276919261418879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.063 × 10¹⁰⁰(101-digit number)

10631490883189263215…78833276919261418881

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

2.126 × 10¹⁰⁰(101-digit number)

21262981766378526430…57666553838522837759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.126 × 10¹⁰⁰(101-digit number)

21262981766378526430…57666553838522837761

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

4.252 × 10¹⁰⁰(101-digit number)

42525963532757052861…15333107677045675519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.252 × 10¹⁰⁰(101-digit number)

42525963532757052861…15333107677045675521

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

8.505 × 10¹⁰⁰(101-digit number)

85051927065514105723…30666215354091351039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.505 × 10¹⁰⁰(101-digit number)

85051927065514105723…30666215354091351041

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