Block #418,606

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/25/2014, 12:38:35 AM · Difficulty 10.3853 · 6,390,505 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5941e766db2faf580fef48b1472f3d3609b02bb3b1578e68e4d4426f4eb78d7e

View on Chainz ↗

Height

#418,606

Difficulty

10.385342

Transactions

Size

646 B

Version

Bits

0a62a5c5

Nonce

6,165

Timestamp

2/25/2014, 12:38:35 AM

Confirmations

6,390,505

Mined by

⛏️ P2SHASXb8Msj7tnyLvWQxYzaaZ1YewBxGf64iZ

Merkle Root

2c6d5473716ba1436c59d15e7fbcc31f1e0f269847cffa5db2b2e38c4105a067

Transactions (3)

Coinbase1212d0af9b9c9c…2df2c5b23c1c71

1 in → 1 out9.2800 XPM101 B

ASXb8Msj…BxGf64iZ

216a9ae79ba14f…e9c9350acaa39e

1 in → 2 out5.1570 XPM226 B

Abkp6z5P…hQ5DLwan ANPHtSdB…jchFMkyy

6778a14336d3d8…b65e3efa4ee0f8

1 in → 2 out2.1268 XPM227 B

AS7Qodvw…SrnR4Skw AMU8nEj9…Eo32pqxr

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.

2.727 × 10⁹⁹(100-digit number)

27273667111205948888…61477433038775982499

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

2.727 × 10⁹⁹(100-digit number)

27273667111205948888…61477433038775982499

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.727 × 10⁹⁹(100-digit number)

27273667111205948888…61477433038775982501

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

5.454 × 10⁹⁹(100-digit number)

54547334222411897777…22954866077551964999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.454 × 10⁹⁹(100-digit number)

54547334222411897777…22954866077551965001

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

1.090 × 10¹⁰⁰(101-digit number)

10909466844482379555…45909732155103929999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.090 × 10¹⁰⁰(101-digit number)

10909466844482379555…45909732155103930001

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

2.181 × 10¹⁰⁰(101-digit number)

21818933688964759111…91819464310207859999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.181 × 10¹⁰⁰(101-digit number)

21818933688964759111…91819464310207860001

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

4.363 × 10¹⁰⁰(101-digit number)

43637867377929518222…83638928620415719999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.363 × 10¹⁰⁰(101-digit number)

43637867377929518222…83638928620415720001

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 #418,606

Cookie Preferences