Block #1,527,731

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/5/2016, 4:02:41 PM · Difficulty 10.6080 · 5,290,090 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

19f9b5e57569920f8e718930a5da7c953f8071d0f5ab9289d39a5c468835332f

View on Chainz ↗

Height

#1,527,731

Difficulty

10.607986

Transactions

Size

1.74 KB

Version

Bits

0a9ba4fa

Nonce

176,028,862

Timestamp

4/5/2016, 4:02:41 PM

Confirmations

5,290,090

Mined by

⛏️ P2SHAQRefeT64fuqJGZjaBrV6YX59qcXr5Utpf

Merkle Root

2e4a8dc1d9bc015efa00c7d48132d3c9ac97dc6bbd98d5ba80c47f2af35a87f5

Transactions (2)

Coinbase454d0b29a7b851…66974cb2bab0d3

1 in → 1 out8.8900 XPM109 B

AQRefeT6…cXr5Utpf

12f3278dd64cc9…6697a4689c18ae

1 in → 42 out17.8656 XPM1.55 KB

Ab8wxBvW…iiDgN5Aa Af6SYSve…4hQNfMLd ANyN2o3Y…Xi5PZr5W AVVtwtxn…G7YjgcAJ ASG21nzq…iMYaGLq3

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.

5.061 × 10⁹⁶(97-digit number)

50619013006562569208…25543834684089769599

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

5.061 × 10⁹⁶(97-digit number)

50619013006562569208…25543834684089769599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.061 × 10⁹⁶(97-digit number)

50619013006562569208…25543834684089769601

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

1.012 × 10⁹⁷(98-digit number)

10123802601312513841…51087669368179539199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.012 × 10⁹⁷(98-digit number)

10123802601312513841…51087669368179539201

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

2.024 × 10⁹⁷(98-digit number)

20247605202625027683…02175338736359078399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.024 × 10⁹⁷(98-digit number)

20247605202625027683…02175338736359078401

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

4.049 × 10⁹⁷(98-digit number)

40495210405250055366…04350677472718156799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.049 × 10⁹⁷(98-digit number)

40495210405250055366…04350677472718156801

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

8.099 × 10⁹⁷(98-digit number)

80990420810500110733…08701354945436313599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.099 × 10⁹⁷(98-digit number)

80990420810500110733…08701354945436313601

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 #1,527,731

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