Block #457,206

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/23/2014, 5:42:50 PM · Difficulty 10.4216 · 6,334,788 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

83a572dbf6be85efb0ffd73d5b2dbf3f4629cd5c163492cad4dd4e6765807abd

View on Chainz ↗

Height

#457,206

Difficulty

10.421650

Transactions

Size

1.39 KB

Version

Bits

0a6bf13d

Nonce

49,191

Timestamp

3/23/2014, 5:42:50 PM

Confirmations

6,334,788

Merkle Root

ca959497277d22e343adadb9d5a5b819ddfcfbe9bfd530accff6bb838f626a34

Transactions (4)

Coinbasebba3ab4807b3d0…6e4bcf297fa0ae

1 in → 1 out9.2200 XPM101 B

ASXb8Msj…BxGf64iZ

c284826d60f839…f92843df71dfc4

1 in → 6 out32.8800 XPM362 B

AerL35yq…gE1jPnhy AYmXDTRZ…RjoLiimC AJiUWmxX…BMH9Vzvt AQe12e3Z…HeWcXVsQ AUoAjuAg…oYcX3CJZ

03f8c0c8a3c1b1…f1e8df6935e783

1 in → 6 out20.8700 XPM361 B

AerL35yq…gE1jPnhy AYmXDTRZ…RjoLiimC AJiUWmxX…BMH9Vzvt AdLfCHKD…GPAdc5Ni AQe12e3Z…HeWcXVsQ

2254c596bd6d5d…bc16bfb4d30080

2 in → 6 out13.8266 XPM509 B

AerL35yq…gE1jPnhy AYmXDTRZ…RjoLiimC AJiUWmxX…BMH9Vzvt Ae725PUt…dukbkgAB AQe12e3Z…HeWcXVsQ

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.

2.573 × 10⁹³(94-digit number)

25731512486342364612…37882252648300117759

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

2.573 × 10⁹³(94-digit number)

25731512486342364612…37882252648300117759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.573 × 10⁹³(94-digit number)

25731512486342364612…37882252648300117761

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

5.146 × 10⁹³(94-digit number)

51463024972684729224…75764505296600235519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.146 × 10⁹³(94-digit number)

51463024972684729224…75764505296600235521

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

1.029 × 10⁹⁴(95-digit number)

10292604994536945844…51529010593200471039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.029 × 10⁹⁴(95-digit number)

10292604994536945844…51529010593200471041

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

2.058 × 10⁹⁴(95-digit number)

20585209989073891689…03058021186400942079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.058 × 10⁹⁴(95-digit number)

20585209989073891689…03058021186400942081

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

4.117 × 10⁹⁴(95-digit number)

41170419978147783379…06116042372801884159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.117 × 10⁹⁴(95-digit number)

41170419978147783379…06116042372801884161

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