Block #1,590,029

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/18/2016, 12:34:01 PM · Difficulty 10.6542 · 5,222,977 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d84433f8f270603f0cc77eb351841dde43e132df1ca56a052dfa443935f32581

View on Chainz ↗

Height

#1,590,029

Difficulty

10.654197

Transactions

Size

573 B

Version

Bits

0aa77979

Nonce

359,086,927

Timestamp

5/18/2016, 12:34:01 PM

Confirmations

5,222,977

Mined by

⛏️ P2SHAamEJHQaJbN5pb1T8x7VApCXswyVozi84y

Merkle Root

0e6370a7bbf1ff23826410ae37649d892141785d45a19e45f36e4b22b20c97fe

Transactions (2)

Coinbaseb3588959c808f1…5c3a939f2a8527

1 in → 1 out8.8100 XPM109 B

AamEJHQa…yVozi84y

33c5b5359edbdf…d8018375589a2b

2 in → 2 out0.0915 XPM373 B

AUGhWs1m…FLEyiFFJ ATn65h1d…dKBd9y2D

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.

1.770 × 10⁹⁶(97-digit number)

17701889164140483099…20132812861976395519

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

1.770 × 10⁹⁶(97-digit number)

17701889164140483099…20132812861976395519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.770 × 10⁹⁶(97-digit number)

17701889164140483099…20132812861976395521

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

3.540 × 10⁹⁶(97-digit number)

35403778328280966199…40265625723952791039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.540 × 10⁹⁶(97-digit number)

35403778328280966199…40265625723952791041

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

7.080 × 10⁹⁶(97-digit number)

70807556656561932399…80531251447905582079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.080 × 10⁹⁶(97-digit number)

70807556656561932399…80531251447905582081

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

1.416 × 10⁹⁷(98-digit number)

14161511331312386479…61062502895811164159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.416 × 10⁹⁷(98-digit number)

14161511331312386479…61062502895811164161

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

2.832 × 10⁹⁷(98-digit number)

28323022662624772959…22125005791622328319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.832 × 10⁹⁷(98-digit number)

28323022662624772959…22125005791622328321

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

5.664 × 10⁹⁷(98-digit number)

56646045325249545919…44250011583244656639

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 #1,590,029

Cookie Preferences