Block #455,030

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/22/2014, 8:05:09 AM · Difficulty 10.4014 · 6,355,949 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

fc69edb44c106979f652c24beae0276a9fb705a78f56f3c749fa66112cb2db8a

View on Chainz ↗

Height

#455,030

Difficulty

10.401435

Transactions

Size

902 B

Version

Bits

0a66c472

Nonce

82,868

Timestamp

3/22/2014, 8:05:09 AM

Confirmations

6,355,949

Mined by

⛏️ vaS-DAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

90975f3935bf27485189e6341e4e6811f160de9ab227c5463c5c84f73e2db6d0

Transactions (1)

Coinbase90975f3935bf27…5c84f73e2db6d0

1 in → 22 out9.2300 XPM811 B

AQvZBsUo…hppgRZTJ ANNg88pG…ppn21sTe ATKK7iFz…wZm46KN1 ALqxX1WA…hsKjbnXn AdhWfaX2…aX7YvEJq

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.

8.678 × 10⁹⁷(98-digit number)

86784847920163215955…33683137207375948959

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

8.678 × 10⁹⁷(98-digit number)

86784847920163215955…33683137207375948959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.678 × 10⁹⁷(98-digit number)

86784847920163215955…33683137207375948961

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

1.735 × 10⁹⁸(99-digit number)

17356969584032643191…67366274414751897919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.735 × 10⁹⁸(99-digit number)

17356969584032643191…67366274414751897921

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

3.471 × 10⁹⁸(99-digit number)

34713939168065286382…34732548829503795839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.471 × 10⁹⁸(99-digit number)

34713939168065286382…34732548829503795841

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

6.942 × 10⁹⁸(99-digit number)

69427878336130572764…69465097659007591679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.942 × 10⁹⁸(99-digit number)

69427878336130572764…69465097659007591681

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

1.388 × 10⁹⁹(100-digit number)

13885575667226114552…38930195318015183359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.388 × 10⁹⁹(100-digit number)

13885575667226114552…38930195318015183361

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 #455,030

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