Block #1,907,174

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/23/2016, 2:29:15 PM · Difficulty 10.7623 · 4,936,866 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d06b3f7868340e83e51ee2967e0260865ecfbe1dac51529232f7d0d9b1502cb5

View on Chainz ↗

Height

#1,907,174

Difficulty

10.762269

Transactions

Size

1.99 KB

Version

Bits

0ac32415

Nonce

592,449,536

Timestamp

12/23/2016, 2:29:15 PM

Confirmations

4,936,866

Mined by

⛏️ P2SHAVNN5buQdKUxCx2ayhmZqJ2qbS5Yh6sbvu

Merkle Root

069be7aab47e8b161f2a3dedf99fe86d63c87a14be457e654acbaa9a5c5f6ca3

Transactions (5)

Coinbasef675ec934eadfa…ceb8daaebc7de9

1 in → 1 out8.6700 XPM110 B

AVNN5buQ…5Yh6sbvu

7310dfba43212e…d604a45777e3a3

8 in → 2 out1405.7486 XPM1.23 KB

AVtWEnxx…nytVBavj AVNTBtZ1…v6S3GT3X

f82f6d144c390c…fb48517f08a784

1 in → 2 out8.8400 XPM193 B

AdQVyW6h…woPp73cj AeYGMGtb…rQ4eQckz

8da07ebb980001…1c0bcfbaca2470

1 in → 2 out8.5800 XPM192 B

Ab9t2pPJ…MYFiK6im AdQVyW6h…woPp73cj

c388c0ad782f89…a2705e83ab572e

1 in → 2 out8.5800 XPM193 B

AdQVyW6h…woPp73cj AKci7Pta…pKDCp5YS

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.

2.042 × 10⁹⁸(99-digit number)

20422220325121663231…78206518970129448959

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

2.042 × 10⁹⁸(99-digit number)

20422220325121663231…78206518970129448959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.042 × 10⁹⁸(99-digit number)

20422220325121663231…78206518970129448961

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

4.084 × 10⁹⁸(99-digit number)

40844440650243326462…56413037940258897919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.084 × 10⁹⁸(99-digit number)

40844440650243326462…56413037940258897921

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

8.168 × 10⁹⁸(99-digit number)

81688881300486652925…12826075880517795839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.168 × 10⁹⁸(99-digit number)

81688881300486652925…12826075880517795841

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

1.633 × 10⁹⁹(100-digit number)

16337776260097330585…25652151761035591679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.633 × 10⁹⁹(100-digit number)

16337776260097330585…25652151761035591681

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

3.267 × 10⁹⁹(100-digit number)

32675552520194661170…51304303522071183359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.267 × 10⁹⁹(100-digit number)

32675552520194661170…51304303522071183361

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 #1,907,174

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