Block #604,336

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 6/27/2014, 5:34:51 PM · Difficulty 10.9105 · 6,199,097 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

744c17b69fc6e6201fb757145fcb48fcb0244d1311123f1718efaba2d1bb22a3

View on Chainz ↗

Height

#604,336

Difficulty

10.910532

Transactions

Size

400 B

Version

Bits

0ae91899

Nonce

293,937,650

Timestamp

6/27/2014, 5:34:51 PM

Confirmations

6,199,097

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

6ed5912cb2d40ec6b143a48b7d44bc2658ec946e91737601a5d8e19f55e742f2

Transactions (2)

Coinbase769993ee88801f…6c61bf73fbee9b

1 in → 1 out8.4001 XPM116 B

ANSXnLY2…Sd25TjkD

725993ebfe7525…99eb668da1e335

1 in → 1 out1.5000 XPM191 B

AdX1TZ55…uMJ4wnv5

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.

1.442 × 10¹⁰¹(102-digit number)

14425897791308187833…06626063488513474559

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

1.442 × 10¹⁰¹(102-digit number)

14425897791308187833…06626063488513474559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.442 × 10¹⁰¹(102-digit number)

14425897791308187833…06626063488513474561

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

2.885 × 10¹⁰¹(102-digit number)

28851795582616375666…13252126977026949119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.885 × 10¹⁰¹(102-digit number)

28851795582616375666…13252126977026949121

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

5.770 × 10¹⁰¹(102-digit number)

57703591165232751333…26504253954053898239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.770 × 10¹⁰¹(102-digit number)

57703591165232751333…26504253954053898241

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

1.154 × 10¹⁰²(103-digit number)

11540718233046550266…53008507908107796479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.154 × 10¹⁰²(103-digit number)

11540718233046550266…53008507908107796481

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

2.308 × 10¹⁰²(103-digit number)

23081436466093100533…06017015816215592959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.308 × 10¹⁰²(103-digit number)

23081436466093100533…06017015816215592961

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

4.616 × 10¹⁰²(103-digit number)

46162872932186201067…12034031632431185919

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