Block #417,598

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/24/2014, 6:57:52 AM · Difficulty 10.3913 · 6,400,304 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9a46bb35b34c05150b512c41646a51e6ed2c35f1c766e4c6a24bb7dc202ed44d

View on Chainz ↗

Height

#417,598

Difficulty

10.391330

Transactions

Size

1.25 KB

Version

Bits

0a642e3b

Nonce

551,323

Timestamp

2/24/2014, 6:57:52 AM

Confirmations

6,400,304

Mined by

⛏️ >_aSAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

a3e524331d207d1efcdbc7777bd56b77dcfaa25366803599f0b17c2b420dea75

Transactions (2)

Coinbase4fbb9b540478b0…f56ef663bdc061

1 in → 22 out9.2500 XPM811 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AYtDvcGs…VuAcA7m7 AGKhfQo2…h7fBXLX6 AZV4TwxQ…8JnQqSoH

f34bb48661c92c…4c0ddda2b95af2

2 in → 2 out1.1506 XPM374 B

AQxzhaK1…9MuQaRdF Aei2GMQ6…MxLiA6Dk

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.

1.887 × 10⁹⁶(97-digit number)

18871919001798358979…36016648642281433599

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

1.887 × 10⁹⁶(97-digit number)

18871919001798358979…36016648642281433599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.887 × 10⁹⁶(97-digit number)

18871919001798358979…36016648642281433601

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

3.774 × 10⁹⁶(97-digit number)

37743838003596717958…72033297284562867199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.774 × 10⁹⁶(97-digit number)

37743838003596717958…72033297284562867201

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

7.548 × 10⁹⁶(97-digit number)

75487676007193435916…44066594569125734399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.548 × 10⁹⁶(97-digit number)

75487676007193435916…44066594569125734401

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

1.509 × 10⁹⁷(98-digit number)

15097535201438687183…88133189138251468799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.509 × 10⁹⁷(98-digit number)

15097535201438687183…88133189138251468801

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

3.019 × 10⁹⁷(98-digit number)

30195070402877374366…76266378276502937599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.019 × 10⁹⁷(98-digit number)

30195070402877374366…76266378276502937601

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 #417,598

Cookie Preferences