Block #566,686

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/29/2014, 2:16:06 AM · Difficulty 10.9661 · 6,225,068 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

948dc5975190adca7986c8e8a74646b8287ed1ba21d6efd6380c7b525615c0c2

View on Chainz ↗

Height

#566,686

Difficulty

10.966070

Transactions

Size

2.02 KB

Version

Bits

0af7505e

Nonce

13,451,905

Timestamp

5/29/2014, 2:16:06 AM

Confirmations

6,225,068

Merkle Root

74421a6d65caaa244807909de4802e22248b693cd63089914360b307ffd71ab7

Transactions (4)

Coinbasecf096881349f23…46b1afe91b4b6d

1 in → 1 out8.3400 XPM116 B

ANSXnLY2…Sd25TjkD

47bf40306d1617…ecd54ab80df4b1

1 in → 2 out8.2900 XPM226 B

ASpQS8U1…Dp8SzLnZ AZxkSxov…9uoWycVz

4af787705b3b0a…19beced8f0a478

1 in → 2 out8.2900 XPM225 B

AS9ZCvju…bu3NEFwZ AR4FxY6U…sjh9gEJD

db33ce686c13ba…cedb6d49fe945f

9 in → 2 out50.5380 XPM1.38 KB

AWi9bZTK…5YAbyMqs AX1JFwLh…8X64XazL

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.

7.900 × 10⁹⁸(99-digit number)

79008076310826739066…81998726850679234559

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

7.900 × 10⁹⁸(99-digit number)

79008076310826739066…81998726850679234559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.900 × 10⁹⁸(99-digit number)

79008076310826739066…81998726850679234561

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

1.580 × 10⁹⁹(100-digit number)

15801615262165347813…63997453701358469119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.580 × 10⁹⁹(100-digit number)

15801615262165347813…63997453701358469121

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

3.160 × 10⁹⁹(100-digit number)

31603230524330695626…27994907402716938239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.160 × 10⁹⁹(100-digit number)

31603230524330695626…27994907402716938241

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

6.320 × 10⁹⁹(100-digit number)

63206461048661391252…55989814805433876479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.320 × 10⁹⁹(100-digit number)

63206461048661391252…55989814805433876481

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

1.264 × 10¹⁰⁰(101-digit number)

12641292209732278250…11979629610867752959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.264 × 10¹⁰⁰(101-digit number)

12641292209732278250…11979629610867752961

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