Block #584,626

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 6/11/2014, 2:55:16 PM · Difficulty 10.9547 · 6,206,690 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6fe077ce17037f4c2e1e3ff1989b9eaf40181a2119d9444a37366aac14eab735

View on Chainz ↗

Height

#584,626

Difficulty

10.954735

Transactions

Size

435 B

Version

Bits

0af4697f

Nonce

1,224,826,257

Timestamp

6/11/2014, 2:55:16 PM

Confirmations

6,206,690

Merkle Root

ea4062a1fde5935bb947d3d7d78b4ce6b411df5b1afd66ddd58abe86643bf942

Transactions (2)

Coinbasee3e2672ec93c07…de235f662dd19c

1 in → 1 out8.3300 XPM116 B

ANSXnLY2…Sd25TjkD

3d4d5624615ff2…78f77dbac30763

1 in → 2 out8.2900 XPM227 B

AGxMeQpn…PtE4vAxN AG7iDgW3…DenKyp4b

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.

1.532 × 10⁹⁹(100-digit number)

15325662262594779602…03264109222684221439

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

1.532 × 10⁹⁹(100-digit number)

15325662262594779602…03264109222684221439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.532 × 10⁹⁹(100-digit number)

15325662262594779602…03264109222684221441

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

3.065 × 10⁹⁹(100-digit number)

30651324525189559205…06528218445368442879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.065 × 10⁹⁹(100-digit number)

30651324525189559205…06528218445368442881

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

6.130 × 10⁹⁹(100-digit number)

61302649050379118411…13056436890736885759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.130 × 10⁹⁹(100-digit number)

61302649050379118411…13056436890736885761

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

1.226 × 10¹⁰⁰(101-digit number)

12260529810075823682…26112873781473771519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.226 × 10¹⁰⁰(101-digit number)

12260529810075823682…26112873781473771521

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

2.452 × 10¹⁰⁰(101-digit number)

24521059620151647364…52225747562947543039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.452 × 10¹⁰⁰(101-digit number)

24521059620151647364…52225747562947543041

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

4.904 × 10¹⁰⁰(101-digit number)

49042119240303294729…04451495125895086079

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