Block #2,635,589

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 4/29/2018, 7:17:05 AM · Difficulty 11.3264 · 4,198,052 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

bc839b55cd05b82d161426d9cf23c3bc6eb1a052be227b67e24476655e2237ab

View on Chainz ↗

Height

#2,635,589

Difficulty

11.326427

Transactions

Size

1.01 KB

Version

Bits

0b5390b1

Nonce

1,628,325,426

Timestamp

4/29/2018, 7:17:05 AM

Confirmations

4,198,052

Mined by

⛏️ P2SHAeYYVJvfzDHwcUyCbDZbXtqeX9JWXWKyCL

Merkle Root

028004efcd0694b5e6e51f733842c8f708b38358497dc9751a5fc4f9dc3e01f9

Transactions (5)

Coinbase34cd336a223441…ca94ea3a838c16

1 in → 1 out7.8200 XPM110 B

AeYYVJvf…JWXWKyCL

3bc7c8049ccbe6…3f6a755db2ef14

1 in → 2 out7.9800 XPM192 B

ANMSxxqk…qDhTJbPR AX3rxQXW…r43ypFZx

8911007487de5b…9676b2d28766b9

1 in → 2 out7.9800 XPM193 B

AX6P4SG8…QbXCyjVM ARJTFmXi…9mT6237k

fd8ea86e6cac45…1bae97775c0493

1 in → 2 out3.9068 XPM225 B

AaxCraKt…CEBafb4N AGnmeBKT…is8wp7ZK

bf8df0cfd79bec…cf93ec3227e7d9

1 in → 2 out2.0066 XPM226 B

ANwtSRNc…za9KnLoD ANxECgWU…JwDdvaP1

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.

1.068 × 10⁹⁶(97-digit number)

10686781781665920688…24682055677657999999

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

1.068 × 10⁹⁶(97-digit number)

10686781781665920688…24682055677657999999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.068 × 10⁹⁶(97-digit number)

10686781781665920688…24682055677658000001

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

2.137 × 10⁹⁶(97-digit number)

21373563563331841376…49364111355315999999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.137 × 10⁹⁶(97-digit number)

21373563563331841376…49364111355316000001

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

4.274 × 10⁹⁶(97-digit number)

42747127126663682753…98728222710631999999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.274 × 10⁹⁶(97-digit number)

42747127126663682753…98728222710632000001

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

8.549 × 10⁹⁶(97-digit number)

85494254253327365507…97456445421263999999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.549 × 10⁹⁶(97-digit number)

85494254253327365507…97456445421264000001

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

1.709 × 10⁹⁷(98-digit number)

17098850850665473101…94912890842527999999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.709 × 10⁹⁷(98-digit number)

17098850850665473101…94912890842528000001

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

3.419 × 10⁹⁷(98-digit number)

34197701701330946203…89825781685055999999

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 #2,635,589

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