Block #590,178

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/16/2014, 2:33:48 AM · Difficulty 10.9460 · 6,218,667 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d0f59c43289f87ec6854eef6f3cd2aadc238503c3942aae2c4bb5cc1f31ba774

View on Chainz ↗

Height

#590,178

Difficulty

10.945975

Transactions

Size

885 B

Version

Bits

0af22b6d

Nonce

829,667,285

Timestamp

6/16/2014, 2:33:48 AM

Confirmations

6,218,667

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

23521adeeb661eadf0a35612b74993d10f9c1c4fb1421ba54ae6d07a18d9797a

Transactions (4)

Coinbase858fa3e9b23ecd…ff3c6e3f3493a3

1 in → 1 out8.3600 XPM116 B

ANSXnLY2…Sd25TjkD

aec70330b9cc35…163ecf0c1a59c6

1 in → 2 out6.2330 XPM226 B

ASkuboV8…mBQxNm3J AdwovpF6…6vVPP8mU

b1122bbf1792ce…bfd763109d7758

1 in → 2 out5.4415 XPM226 B

AT4jiN6n…xhwHiNyJ AcB1Cdou…cFjow1c5

dd05befc2538b8…56469d45576cce

1 in → 2 out2.1384 XPM226 B

Ac8Sz9oB…w9RHvJc8 AWeFTqSF…usRDA3NM

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.

1.878 × 10⁹⁷(98-digit number)

18787559464976467579…29110467812245527829

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

1.878 × 10⁹⁷(98-digit number)

18787559464976467579…29110467812245527829

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.878 × 10⁹⁷(98-digit number)

18787559464976467579…29110467812245527831

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

3.757 × 10⁹⁷(98-digit number)

37575118929952935159…58220935624491055659

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.757 × 10⁹⁷(98-digit number)

37575118929952935159…58220935624491055661

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

7.515 × 10⁹⁷(98-digit number)

75150237859905870319…16441871248982111319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.515 × 10⁹⁷(98-digit number)

75150237859905870319…16441871248982111321

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

1.503 × 10⁹⁸(99-digit number)

15030047571981174063…32883742497964222639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.503 × 10⁹⁸(99-digit number)

15030047571981174063…32883742497964222641

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

3.006 × 10⁹⁸(99-digit number)

30060095143962348127…65767484995928445279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.006 × 10⁹⁸(99-digit number)

30060095143962348127…65767484995928445281

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 #590,178

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