Block #471,524

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/2/2014, 3:41:36 PM · Difficulty 10.4344 · 6,327,750 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0eb6ff3f5078d2b94b5f2fda09e3fde792e4941099fb7f9bf16e6a4e1cdddeff

View on Chainz ↗

Height

#471,524

Difficulty

10.434450

Transactions

Size

1.54 KB

Version

Bits

0a6f381b

Nonce

214,850

Timestamp

4/2/2014, 3:41:36 PM

Confirmations

6,327,750

Mined by

AdFLJFhbQJWBJcv1fjoDef6HbwbsaVkAyh

Merkle Root

a6a386d14114d206898bcf02aca49c33ab019abec993635e0834b8a955ad222f

Transactions (4)

Coinbase6a31618ce5c252…4095c463c01b5a

1 in → 22 out9.2000 XPM811 B

AdFLJFhb…bsaVkAyh AGz9gyZW…bo8NYQpw AMW1p9oT…2TzdaZxH ATp4jJhs…TbSgR8Qb AbPcCMg4…719q6mAX

ab46b00eacd65a…c7510f874daf19

1 in → 2 out2970.3151 XPM225 B

AeQDTBUy…pPBdKsbD AJJZDwBv…vDNVjVVq

d14577ea3ed7e5…f32d601ffd3ade

1 in → 2 out7.1383 XPM226 B

AW6er7qf…Wx3eu3gv Aez7nBb5…U4byib9D

f8562debe814e2…176c7256379bcb

1 in → 2 out2.5212 XPM226 B

AdG65wVF…FfKdGajE AXxp24rY…yi3yUFBu

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.

7.063 × 10⁹⁶(97-digit number)

70630091476865045497…40367794821345525759

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

7.063 × 10⁹⁶(97-digit number)

70630091476865045497…40367794821345525759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.063 × 10⁹⁶(97-digit number)

70630091476865045497…40367794821345525761

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

1.412 × 10⁹⁷(98-digit number)

14126018295373009099…80735589642691051519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.412 × 10⁹⁷(98-digit number)

14126018295373009099…80735589642691051521

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

2.825 × 10⁹⁷(98-digit number)

28252036590746018199…61471179285382103039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.825 × 10⁹⁷(98-digit number)

28252036590746018199…61471179285382103041

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

5.650 × 10⁹⁷(98-digit number)

56504073181492036398…22942358570764206079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.650 × 10⁹⁷(98-digit number)

56504073181492036398…22942358570764206081

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

1.130 × 10⁹⁸(99-digit number)

11300814636298407279…45884717141528412159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.130 × 10⁹⁸(99-digit number)

11300814636298407279…45884717141528412161

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