Block #1,354,546

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/4/2015, 8:20:04 PM · Difficulty 10.8058 · 5,472,769 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d58096e4dce2995e0ded659b545e747eb7dada0bb885dbe6b152ed9af60bc1e1

View on Chainz ↗

Height

#1,354,546

Difficulty

10.805795

Transactions

Size

244 B

Version

Bits

0ace4891

Nonce

76,669,945

Timestamp

12/4/2015, 8:20:04 PM

Confirmations

5,472,769

Mined by

⛏️ P2SHAUosZTYjuWtKFSMDF2U5GniQyrHEUT5qBD

Merkle Root

5ddd1a6983d3d1c8de6586f36f604b5e00d7a098535caa97e3b5981984f81287

Transactions (1)

Coinbase5ddd1a6983d3d1…b5981984f81287

1 in → 2 out8.5500 XPM152 B

AUosZTYj…HEUT5qBD ALPu3s2c…EJXLjVFh

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.

9.838 × 10⁹⁸(99-digit number)

98380442079032584483…19609460660746813439

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

9.838 × 10⁹⁸(99-digit number)

98380442079032584483…19609460660746813439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.838 × 10⁹⁸(99-digit number)

98380442079032584483…19609460660746813441

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

1.967 × 10⁹⁹(100-digit number)

19676088415806516896…39218921321493626879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.967 × 10⁹⁹(100-digit number)

19676088415806516896…39218921321493626881

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

3.935 × 10⁹⁹(100-digit number)

39352176831613033793…78437842642987253759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.935 × 10⁹⁹(100-digit number)

39352176831613033793…78437842642987253761

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

7.870 × 10⁹⁹(100-digit number)

78704353663226067587…56875685285974507519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.870 × 10⁹⁹(100-digit number)

78704353663226067587…56875685285974507521

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

1.574 × 10¹⁰⁰(101-digit number)

15740870732645213517…13751370571949015039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.574 × 10¹⁰⁰(101-digit number)

15740870732645213517…13751370571949015041

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 #1,354,546

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