Block #599,265

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 6/23/2014, 11:16:38 AM · Difficulty 10.9274 · 6,227,726 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

43145bd681f47574d03b70be6331024452de4b367183c97e23fbec1bfe25d0f6

View on Chainz ↗

Height

#599,265

Difficulty

10.927408

Transactions

Size

878 B

Version

Bits

0aed6a9a

Nonce

75,573,504

Timestamp

6/23/2014, 11:16:38 AM

Confirmations

6,227,726

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

70ca292acda23180fc75c5ecc298c0d684e37ac76c97016d1a78cd3df45a3a48

Transactions (2)

Coinbasee92ea220784652…fdb6c93685c148

1 in → 1 out8.3700 XPM116 B

ANSXnLY2…Sd25TjkD

418f7271b7296a…09ec6444248d9c

4 in → 2 out7.1786 XPM671 B

AeFkKQRX…aTovnqjS AZS4yuXr…deWqZ51K

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.

8.313 × 10⁹⁷(98-digit number)

83134999368085966578…04073604294050735999

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

8.313 × 10⁹⁷(98-digit number)

83134999368085966578…04073604294050735999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.313 × 10⁹⁷(98-digit number)

83134999368085966578…04073604294050736001

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

1.662 × 10⁹⁸(99-digit number)

16626999873617193315…08147208588101471999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.662 × 10⁹⁸(99-digit number)

16626999873617193315…08147208588101472001

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

3.325 × 10⁹⁸(99-digit number)

33253999747234386631…16294417176202943999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.325 × 10⁹⁸(99-digit number)

33253999747234386631…16294417176202944001

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

6.650 × 10⁹⁸(99-digit number)

66507999494468773262…32588834352405887999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.650 × 10⁹⁸(99-digit number)

66507999494468773262…32588834352405888001

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

1.330 × 10⁹⁹(100-digit number)

13301599898893754652…65177668704811775999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.330 × 10⁹⁹(100-digit number)

13301599898893754652…65177668704811776001

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

2.660 × 10⁹⁹(100-digit number)

26603199797787509305…30355337409623551999

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 #599,265

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