Block #471,486

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/2/2014, 2:58:47 PM · Difficulty 10.4351 · 6,321,259 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

899d58945199a1d1d124b00f4ef4607cc0e5e4eea33dda3733903819773c9b1e

View on Chainz ↗

Height

#471,486

Difficulty

10.435073

Transactions

Size

655 B

Version

Bits

0a6f60f6

Nonce

341,115

Timestamp

4/2/2014, 2:58:47 PM

Confirmations

6,321,259

Merkle Root

82ed0e9a9cd92107b45c3c692808da1da72adaac27bda60b9c44babb538c9d8e

Transactions (3)

Coinbasedc692b2ece76d7…cca8b54a06cf31

1 in → 1 out9.1900 XPM111 B

ARDxAPMv…DFfgpVY2

07ed2d43a7f1c3…ca3d9ad75af235

1 in → 2 out4414.8710 XPM226 B

ALYm4N2u…TLZ3XMjf Af65eaxX…ZJL5htZ3

4ab10e313acdbb…40a642d3e3fc46

1 in → 2 out2.0627 XPM226 B

AR3bcP9T…74Xf4vmQ ANKVK6Uv…mSZV2UkB

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.

3.626 × 10⁹⁸(99-digit number)

36261580575602462184…70840622711017727999

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

3.626 × 10⁹⁸(99-digit number)

36261580575602462184…70840622711017727999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.626 × 10⁹⁸(99-digit number)

36261580575602462184…70840622711017728001

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

7.252 × 10⁹⁸(99-digit number)

72523161151204924368…41681245422035455999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.252 × 10⁹⁸(99-digit number)

72523161151204924368…41681245422035456001

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

1.450 × 10⁹⁹(100-digit number)

14504632230240984873…83362490844070911999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.450 × 10⁹⁹(100-digit number)

14504632230240984873…83362490844070912001

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

2.900 × 10⁹⁹(100-digit number)

29009264460481969747…66724981688141823999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.900 × 10⁹⁹(100-digit number)

29009264460481969747…66724981688141824001

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

5.801 × 10⁹⁹(100-digit number)

58018528920963939494…33449963376283647999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.801 × 10⁹⁹(100-digit number)

58018528920963939494…33449963376283648001

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