Block #593,848

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/19/2014, 1:18:14 AM · Difficulty 10.9396 · 6,202,118 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5f7b578e7518349bfabb761f3cce79b88a65a2a42bb5d8a6704fee868ad8de16

View on Chainz ↗

Height

#593,848

Difficulty

10.939602

Transactions

Size

1.01 KB

Version

Bits

0af089c9

Nonce

695,428,748

Timestamp

6/19/2014, 1:18:14 AM

Confirmations

6,202,118

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

edf9384c1ba0021202b240dff43064ecb64924d3b13d20965cec1207467bd9e4

Transactions (4)

Coinbase007f019cf9a83c…1e9bba870e97ac

1 in → 1 out8.3700 XPM116 B

ANSXnLY2…Sd25TjkD

1f118612820dd1…8e0fb01cbfde3b

1 in → 2 out8.3100 XPM226 B

AdevTCb4…jewFe724 AWeFTqSF…usRDA3NM

7af7f49dd78773…be7215bf9d3996

2 in → 2 out15.6494 XPM375 B

AT6KDmkT…S6R6v2ER AL9qWuWF…w9Kk2n6r

31dc6deee99c26…5d9e622888f99a

1 in → 2 out7.5988 XPM225 B

ANYrTopX…iPGS68CF AWAwVNg1…ezF8WmBs

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.

7.551 × 10⁹⁶(97-digit number)

75518734854404656244…33370117251101616079

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

7.551 × 10⁹⁶(97-digit number)

75518734854404656244…33370117251101616079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.551 × 10⁹⁶(97-digit number)

75518734854404656244…33370117251101616081

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

1.510 × 10⁹⁷(98-digit number)

15103746970880931248…66740234502203232159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.510 × 10⁹⁷(98-digit number)

15103746970880931248…66740234502203232161

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

3.020 × 10⁹⁷(98-digit number)

30207493941761862497…33480469004406464319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.020 × 10⁹⁷(98-digit number)

30207493941761862497…33480469004406464321

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

6.041 × 10⁹⁷(98-digit number)

60414987883523724995…66960938008812928639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.041 × 10⁹⁷(98-digit number)

60414987883523724995…66960938008812928641

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

1.208 × 10⁹⁸(99-digit number)

12082997576704744999…33921876017625857279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.208 × 10⁹⁸(99-digit number)

12082997576704744999…33921876017625857281

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