Block #626,159

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 7/10/2014, 2:17:06 AM · Difficulty 10.9602 · 6,182,102 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a9e8e55eb201eca1fe1778d29b9cf8409e0f552355d3d0de9d19c4c2491cc94c

View on Chainz ↗

Height

#626,159

Difficulty

10.960184

Transactions

Size

433 B

Version

Bits

0af5ce98

Nonce

43,175,062

Timestamp

7/10/2014, 2:17:06 AM

Confirmations

6,182,102

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

b055bc2f311943c87f42e343169bfce5348c636fc4ca8f84cb6a72f08e616d23

Transactions (2)

Coinbase879c61c481faff…c76348e7d935e2

1 in → 1 out8.3200 XPM116 B

ANSXnLY2…Sd25TjkD

018aa61cc343c2…14bf9888ded501

1 in → 2 out6.7464 XPM225 B

AW7k2MZd…9b8YznyG AKoEWNKr…CQjmDyvq

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.

4.157 × 10⁹⁸(99-digit number)

41577244757337176943…42986296146906992639

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

4.157 × 10⁹⁸(99-digit number)

41577244757337176943…42986296146906992639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.157 × 10⁹⁸(99-digit number)

41577244757337176943…42986296146906992641

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

8.315 × 10⁹⁸(99-digit number)

83154489514674353887…85972592293813985279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.315 × 10⁹⁸(99-digit number)

83154489514674353887…85972592293813985281

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

1.663 × 10⁹⁹(100-digit number)

16630897902934870777…71945184587627970559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.663 × 10⁹⁹(100-digit number)

16630897902934870777…71945184587627970561

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

3.326 × 10⁹⁹(100-digit number)

33261795805869741554…43890369175255941119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.326 × 10⁹⁹(100-digit number)

33261795805869741554…43890369175255941121

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

6.652 × 10⁹⁹(100-digit number)

66523591611739483109…87780738350511882239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.652 × 10⁹⁹(100-digit number)

66523591611739483109…87780738350511882241

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

1.330 × 10¹⁰⁰(101-digit number)

13304718322347896621…75561476701023764479

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

Block #626,159

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