Block #592,185

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 6/17/2014, 4:15:01 PM · Difficulty 10.9433 · 6,204,476 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

42fb83a01cc181934927b783b34504e6b1a3f1b0c610914b29199a2ad1f8aaf5

View on Chainz ↗

Height

#592,185

Difficulty

10.943273

Transactions

Size

6.07 KB

Version

Bits

0af17a59

Nonce

52,970,130

Timestamp

6/17/2014, 4:15:01 PM

Confirmations

6,204,476

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

46bcfa07faa56b97f8a5002ea66c8ea48d9816766300765bf34b83afb870082a

Transactions (4)

Coinbase4af1be988d7dc2…20e09bfbcec88c

1 in → 1 out8.4200 XPM116 B

ANSXnLY2…Sd25TjkD

24ce940b1d22e7…758c8ce74fd431

36 in → 2 out10000.0100 XPM5.29 KB

Ae5WFHbn…gBo7rvHr AGm85kxT…4JaikcAD

c955bb861eec59…382e3824c14796

1 in → 2 out3.9566 XPM226 B

AYt5grtd…X2DHMmwW AGZKomZ2…JwPFwkCF

eed5e9137ebe59…e953394937c2c0

2 in → 2 out0.5152 XPM374 B

AVBp6Ymd…JhN931SM AMx9mTdJ…UwM1tSSA

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.

1.162 × 10⁹⁸(99-digit number)

11622479366868476751…39978480611890186079

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

1.162 × 10⁹⁸(99-digit number)

11622479366868476751…39978480611890186079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.162 × 10⁹⁸(99-digit number)

11622479366868476751…39978480611890186081

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

2.324 × 10⁹⁸(99-digit number)

23244958733736953502…79956961223780372159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.324 × 10⁹⁸(99-digit number)

23244958733736953502…79956961223780372161

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

4.648 × 10⁹⁸(99-digit number)

46489917467473907005…59913922447560744319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.648 × 10⁹⁸(99-digit number)

46489917467473907005…59913922447560744321

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

9.297 × 10⁹⁸(99-digit number)

92979834934947814010…19827844895121488639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.297 × 10⁹⁸(99-digit number)

92979834934947814010…19827844895121488641

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

1.859 × 10⁹⁹(100-digit number)

18595966986989562802…39655689790242977279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.859 × 10⁹⁹(100-digit number)

18595966986989562802…39655689790242977281

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

3.719 × 10⁹⁹(100-digit number)

37191933973979125604…79311379580485954559

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