Block #753,801

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 10/6/2014, 2:09:34 AM · Difficulty 10.9704 · 6,064,131 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9d1301888a8657066f53a3eca67d429d8469d987f1736407ce6c9d732d06bf74

View on Chainz ↗

Height

#753,801

Difficulty

10.970389

Transactions

Size

728 B

Version

Bits

0af86b64

Nonce

1,001,940,673

Timestamp

10/6/2014, 2:09:34 AM

Confirmations

6,064,131

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

5da4d0bc427e77a157de0d4841a5c5c4c15efcbf403b446a08144d269adcfcaa

Transactions (3)

Coinbaseeae62f883474f1…2060fc3a986fa2

1 in → 1 out8.3200 XPM116 B

ANSXnLY2…Sd25TjkD

4be43bb0c38eca…dde4f69b3264ba

1 in → 2 out8.2700 XPM227 B

ATUJFkEF…j71DTZhm AUKFsQgo…sR6vSzax

f5dc731c8b121b…b09f8d4b3a8db1

1 in → 4 out7.2961 XPM294 B

ARJQsNEx…UvYvuSPW AHZ6LSRb…otxTNghi AeKNrjNj…1NEq95Ta AJcmFad4…YNAMFS3w

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.

1.861 × 10⁹⁷(98-digit number)

18616800507322105875…53963978655418694399

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

1.861 × 10⁹⁷(98-digit number)

18616800507322105875…53963978655418694399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.861 × 10⁹⁷(98-digit number)

18616800507322105875…53963978655418694401

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

3.723 × 10⁹⁷(98-digit number)

37233601014644211751…07927957310837388799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.723 × 10⁹⁷(98-digit number)

37233601014644211751…07927957310837388801

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

7.446 × 10⁹⁷(98-digit number)

74467202029288423502…15855914621674777599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.446 × 10⁹⁷(98-digit number)

74467202029288423502…15855914621674777601

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

1.489 × 10⁹⁸(99-digit number)

14893440405857684700…31711829243349555199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.489 × 10⁹⁸(99-digit number)

14893440405857684700…31711829243349555201

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

2.978 × 10⁹⁸(99-digit number)

29786880811715369400…63423658486699110399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.978 × 10⁹⁸(99-digit number)

29786880811715369400…63423658486699110401

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

5.957 × 10⁹⁸(99-digit number)

59573761623430738801…26847316973398220799

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 #753,801

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