Block #490,602

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 4/13/2014, 11:29:08 PM · Difficulty 10.6780 · 6,302,378 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

dad8f92e6689fe6146267f095ea2cf00dd75e9606447fdbe7898979715c2684f

View on Chainz ↗

Height

#490,602

Difficulty

10.678017

Transactions

Size

868 B

Version

Bits

0aad9285

Nonce

195,675

Timestamp

4/13/2014, 11:29:08 PM

Confirmations

6,302,378

Merkle Root

d0bd0de45a8d00f5e47cb35746e88a18f31ee8d317b94bf24296330071067547

Transactions (1)

Coinbased0bd0de45a8d00…96330071067547

1 in → 21 out8.7600 XPM777 B

ATKK7iFz…wZm46KN1 AYckRkCF…TgDe5VSp ALqxX1WA…hsKjbnXn ANNg88pG…ppn21sTe AQHMHHp4…HXVnq5H2

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.

1.237 × 10⁹⁷(98-digit number)

12378176890672215558…66531990466704691199

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

1.237 × 10⁹⁷(98-digit number)

12378176890672215558…66531990466704691199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.237 × 10⁹⁷(98-digit number)

12378176890672215558…66531990466704691201

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

2.475 × 10⁹⁷(98-digit number)

24756353781344431116…33063980933409382399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.475 × 10⁹⁷(98-digit number)

24756353781344431116…33063980933409382401

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

4.951 × 10⁹⁷(98-digit number)

49512707562688862232…66127961866818764799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.951 × 10⁹⁷(98-digit number)

49512707562688862232…66127961866818764801

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

9.902 × 10⁹⁷(98-digit number)

99025415125377724464…32255923733637529599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.902 × 10⁹⁷(98-digit number)

99025415125377724464…32255923733637529601

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

1.980 × 10⁹⁸(99-digit number)

19805083025075544892…64511847467275059199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.980 × 10⁹⁸(99-digit number)

19805083025075544892…64511847467275059201

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

3.961 × 10⁹⁸(99-digit number)

39610166050151089785…29023694934550118399

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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