Block #1,469,103

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/23/2016, 6:20:52 AM · Difficulty 10.7565 · 5,327,043 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c88cac6ec7e6a24a1603c145d154f3f54ed10734d68c946188fafa903fe18ad0

View on Chainz ↗

Height

#1,469,103

Difficulty

10.756547

Transactions

Size

426 B

Version

Bits

0ac1ad0c

Nonce

1,125,392,375

Timestamp

2/23/2016, 6:20:52 AM

Confirmations

5,327,043

Mined by

⛏️ P2SHAGRytgZrcpkPLvvvJskxahY1gAuF2UfGyM

Merkle Root

a6a5f75c78898f84061424a033bbb50fa090560445e9e8f279504bf0c00d3baf

Transactions (2)

Coinbase51eaf7306eaa0a…f249a95c8f8706

1 in → 1 out8.6400 XPM109 B

AGRytgZr…uF2UfGyM

a1e7fd5821d571…79d9e914ea01c2

1 in → 2 out2015.2458 XPM226 B

Ad6mLpuL…SVPUUJyT ATNnn9ok…6UTPaJtm

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.

1.132 × 10⁹⁶(97-digit number)

11326707629330022147…60452875181564149759

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

1.132 × 10⁹⁶(97-digit number)

11326707629330022147…60452875181564149759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.132 × 10⁹⁶(97-digit number)

11326707629330022147…60452875181564149761

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

2.265 × 10⁹⁶(97-digit number)

22653415258660044295…20905750363128299519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.265 × 10⁹⁶(97-digit number)

22653415258660044295…20905750363128299521

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

4.530 × 10⁹⁶(97-digit number)

45306830517320088591…41811500726256599039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.530 × 10⁹⁶(97-digit number)

45306830517320088591…41811500726256599041

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

9.061 × 10⁹⁶(97-digit number)

90613661034640177182…83623001452513198079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.061 × 10⁹⁶(97-digit number)

90613661034640177182…83623001452513198081

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

1.812 × 10⁹⁷(98-digit number)

18122732206928035436…67246002905026396159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.812 × 10⁹⁷(98-digit number)

18122732206928035436…67246002905026396161

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