Block #596,882

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 6/21/2014, 11:35:37 AM · Difficulty 10.9339 · 6,211,782 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

29b347400c446ea449de4692580fd8164b9ade6071e70be0fbc27cf148b3ea2c

View on Chainz ↗

Height

#596,882

Difficulty

10.933922

Transactions

Size

494 B

Version

Bits

0aef1584

Nonce

232,950

Timestamp

6/21/2014, 11:35:37 AM

Confirmations

6,211,782

Mined by

⛏️ aSmAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

3fc01c472d748fb752f487becffbc4654bd0608c9853bc0c58c430d7cc2ea5dd

Transactions (1)

Coinbase3fc01c472d748f…c430d7cc2ea5dd

1 in → 10 out8.3500 XPM403 B

AQvZBsUo…hppgRZTJ AJzWx2VD…j4ZSMit5 AJtNW28X…Syb4Ph5j AQyr8Lw3…hs4nt3Pn AJtsGkR4…BuZ5GKQN

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.

2.172 × 10⁹⁶(97-digit number)

21724651366474872941…31569889925459678719

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

2.172 × 10⁹⁶(97-digit number)

21724651366474872941…31569889925459678719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.172 × 10⁹⁶(97-digit number)

21724651366474872941…31569889925459678721

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

4.344 × 10⁹⁶(97-digit number)

43449302732949745883…63139779850919357439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.344 × 10⁹⁶(97-digit number)

43449302732949745883…63139779850919357441

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

8.689 × 10⁹⁶(97-digit number)

86898605465899491766…26279559701838714879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.689 × 10⁹⁶(97-digit number)

86898605465899491766…26279559701838714881

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

1.737 × 10⁹⁷(98-digit number)

17379721093179898353…52559119403677429759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.737 × 10⁹⁷(98-digit number)

17379721093179898353…52559119403677429761

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

3.475 × 10⁹⁷(98-digit number)

34759442186359796706…05118238807354859519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.475 × 10⁹⁷(98-digit number)

34759442186359796706…05118238807354859521

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

6.951 × 10⁹⁷(98-digit number)

69518884372719593413…10236477614709719039

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 #596,882

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