Block #1,065,610

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/19/2015, 1:06:17 AM · Difficulty 10.7336 · 5,729,440 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c7a9a33922522385ce756e3ab4bed22e2a43b6a8ad7b0a4bea2ee63a44a3453b

View on Chainz ↗

Height

#1,065,610

Difficulty

10.733598

Transactions

Size

1.01 KB

Version

Bits

0abbcd1b

Nonce

510,639,412

Timestamp

5/19/2015, 1:06:17 AM

Confirmations

5,729,440

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

15e7f91b1509a6a1f62a79d236fd9dd2152e638df206b859721ba24423fc82f0

Transactions (4)

Coinbase7c1c86c7639d76…752961831710cd

1 in → 1 out8.7000 XPM116 B

ANSXnLY2…Sd25TjkD

b864677649fc83…03bded09c2ddef

1 in → 2 out8.6600 XPM226 B

AGzj2oxs…tUsN2mcG AN9kaPDG…27FmAd51

3e44041a65e923…b898e68db83890

1 in → 2 out8.6600 XPM226 B

Af3aPj7K…cnGd5dnY AKD861U7…FmRtq7Xp

ab0aa440f49723…292b069fdbdbc6

2 in → 2 out11.1275 XPM373 B

Ae9drWdk…FnLTm9Pn AVLHSQvr…fDUYVSDF

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.

1.999 × 10⁹⁶(97-digit number)

19993481802847895278…07037470154038094079

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

1.999 × 10⁹⁶(97-digit number)

19993481802847895278…07037470154038094079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.999 × 10⁹⁶(97-digit number)

19993481802847895278…07037470154038094081

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

3.998 × 10⁹⁶(97-digit number)

39986963605695790556…14074940308076188159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.998 × 10⁹⁶(97-digit number)

39986963605695790556…14074940308076188161

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

7.997 × 10⁹⁶(97-digit number)

79973927211391581113…28149880616152376319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.997 × 10⁹⁶(97-digit number)

79973927211391581113…28149880616152376321

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

1.599 × 10⁹⁷(98-digit number)

15994785442278316222…56299761232304752639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.599 × 10⁹⁷(98-digit number)

15994785442278316222…56299761232304752641

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

3.198 × 10⁹⁷(98-digit number)

31989570884556632445…12599522464609505279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.198 × 10⁹⁷(98-digit number)

31989570884556632445…12599522464609505281

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