Block #2,696,196

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 6/7/2018, 9:59:46 PM · Difficulty 11.6701 · 4,146,058 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2cc1950640f9771a78ef4ffb69e9aa4b00ba0f33bb980a633fb9261e22f639e1

View on Chainz ↗

Height

#2,696,196

Difficulty

11.670067

Transactions

Size

867 B

Version

Bits

0bab8984

Nonce

382,077,787

Timestamp

6/7/2018, 9:59:46 PM

Confirmations

4,146,058

Mined by

⛏️ P2SHAS1W5haEo2StwK8tgiMRMTiojgXKbWFGgt

Merkle Root

4a126e141b7cec9f8972a406f872a2059d4fcfeeb368f4aad71c55fabbb0c50b

Transactions (2)

Coinbase06a80ace03e0db…8a68b610bb503a

1 in → 1 out7.3400 XPM110 B

AS1W5haE…XKbWFGgt

91d8ad35de08e0…6f9617acc5637b

4 in → 2 out2205.0101 XPM667 B

AeqxUzPm…XNyJFSj5 APam1QKu…z5xJrsz1

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.

7.104 × 10⁹⁴(95-digit number)

71043931531740383048…76754822025835118879

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

7.104 × 10⁹⁴(95-digit number)

71043931531740383048…76754822025835118879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.104 × 10⁹⁴(95-digit number)

71043931531740383048…76754822025835118881

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

1.420 × 10⁹⁵(96-digit number)

14208786306348076609…53509644051670237759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.420 × 10⁹⁵(96-digit number)

14208786306348076609…53509644051670237761

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

2.841 × 10⁹⁵(96-digit number)

28417572612696153219…07019288103340475519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.841 × 10⁹⁵(96-digit number)

28417572612696153219…07019288103340475521

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

5.683 × 10⁹⁵(96-digit number)

56835145225392306439…14038576206680951039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.683 × 10⁹⁵(96-digit number)

56835145225392306439…14038576206680951041

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

1.136 × 10⁹⁶(97-digit number)

11367029045078461287…28077152413361902079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.136 × 10⁹⁶(97-digit number)

11367029045078461287…28077152413361902081

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

2.273 × 10⁹⁶(97-digit number)

22734058090156922575…56154304826723804159

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 #2,696,196

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