Block #1,534,683

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/10/2016, 9:59:32 AM · Difficulty 10.6176 · 5,276,292 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

cb84c80a8677a3fdbc7d5b7a98bc06627903243eb35d5a23dfdc1567363fb5a2

View on Chainz ↗

Height

#1,534,683

Difficulty

10.617564

Transactions

Size

15.02 KB

Version

Bits

0a9e18ab

Nonce

53,799,450

Timestamp

4/10/2016, 9:59:32 AM

Confirmations

5,276,292

Mined by

⛏️ P2SHAdsGFJcLdcbFTDBJbxaCxVfthDJa21WSvC

Merkle Root

7feaa005edf7795a7c25082a109aa42b844de32c9de8acad158c30aad761cdc1

Transactions (3)

Coinbasec658d56dd974ce…626c099db47a19

1 in → 1 out9.0200 XPM109 B

AdsGFJcL…Ja21WSvC

3bfd73985aed9e…09a494790cdda8

51 in → 1 out3058.4675 XPM7.41 KB

AYtj13PA…BW7bBB9M

d375d943628b6d…fc3db2cf815983

51 in → 1 out146.0188 XPM7.42 KB

AGPBwpjZ…5pzhkDNn

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.

1.811 × 10⁹⁷(98-digit number)

18110216920472253329…61971059766128025599

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

1.811 × 10⁹⁷(98-digit number)

18110216920472253329…61971059766128025599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.811 × 10⁹⁷(98-digit number)

18110216920472253329…61971059766128025601

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

3.622 × 10⁹⁷(98-digit number)

36220433840944506659…23942119532256051199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.622 × 10⁹⁷(98-digit number)

36220433840944506659…23942119532256051201

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

7.244 × 10⁹⁷(98-digit number)

72440867681889013319…47884239064512102399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.244 × 10⁹⁷(98-digit number)

72440867681889013319…47884239064512102401

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

1.448 × 10⁹⁸(99-digit number)

14488173536377802663…95768478129024204799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.448 × 10⁹⁸(99-digit number)

14488173536377802663…95768478129024204801

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

2.897 × 10⁹⁸(99-digit number)

28976347072755605327…91536956258048409599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.897 × 10⁹⁸(99-digit number)

28976347072755605327…91536956258048409601

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 #1,534,683

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