Block #507,835

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/24/2014, 12:03:52 AM · Difficulty 10.8173 · 6,302,437 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

dbda068341a64ce5f40099627c5f44d57d7d44673b9c944aa328d780de6ea42b

View on Chainz ↗

Height

#507,835

Difficulty

10.817274

Transactions

Size

6.72 KB

Version

Bits

0ad138d9

Nonce

184,361

Timestamp

4/24/2014, 12:03:52 AM

Confirmations

6,302,437

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

43f0667529c00b06f34586f95e02d6e3460d14c26eef85db4f97f6f5ff0aaf2a

Transactions (5)

Coinbase7df27de41026da…246c43a54ea26d

1 in → 1 out8.6200 XPM110 B

AeKNrjNj…1NEq95Ta

56a37ab087c90d…e6e17ab2a6cf5a

38 in → 2 out10.5191 XPM5.57 KB

AJEn77EL…qexZAzRG APXAME9k…Zmi4fYry

ba61bb342106a4…ee2db23ae31b1b

1 in → 2 out5.1052 XPM226 B

AGRrLX34…F9zbreRe AZwmCqXT…hfhhUbpU

b1026a79561ea4…561dc45ff21f4f

1 in → 2 out2.3164 XPM226 B

AdHb8jXC…gMcXX96C AGdWVjRk…LFVsqCnK

39561be1e4673e…46b4ffec8325b6

3 in → 2 out5.2218 XPM520 B

AGnBCf1R…D2a4G1mZ Adv9ey12…sZ5gm2gW

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.

4.787 × 10⁹⁷(98-digit number)

47874150986810148166…54240971982000638879

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

4.787 × 10⁹⁷(98-digit number)

47874150986810148166…54240971982000638879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.787 × 10⁹⁷(98-digit number)

47874150986810148166…54240971982000638881

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

9.574 × 10⁹⁷(98-digit number)

95748301973620296333…08481943964001277759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.574 × 10⁹⁷(98-digit number)

95748301973620296333…08481943964001277761

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

1.914 × 10⁹⁸(99-digit number)

19149660394724059266…16963887928002555519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.914 × 10⁹⁸(99-digit number)

19149660394724059266…16963887928002555521

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

3.829 × 10⁹⁸(99-digit number)

38299320789448118533…33927775856005111039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.829 × 10⁹⁸(99-digit number)

38299320789448118533…33927775856005111041

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

7.659 × 10⁹⁸(99-digit number)

76598641578896237066…67855551712010222079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.659 × 10⁹⁸(99-digit number)

76598641578896237066…67855551712010222081

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #507,835

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