Block #1,196,879

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 8/16/2015, 8:13:45 PM · Difficulty 10.8273 · 5,613,073 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4b1f408b5011fa22ca31ea647d87d71e5a65a93fc5ab4eba3d94d487f2770845

View on Chainz ↗

Height

#1,196,879

Difficulty

10.827306

Transactions

Size

5.11 KB

Version

Bits

0ad3ca4c

Nonce

828,168,155

Timestamp

8/16/2015, 8:13:45 PM

Confirmations

5,613,073

Mined by

⛏️ P2SHAJCEY9yyy2DERzsA24UUtHTMGPtg97E6zm

Merkle Root

11a296d20939bf3e6896586f8eb283e75fd355f221507954492e4fadc6b1f3c7

Transactions (4)

Coinbase1af87ee02fb6b6…b256ffb624996c

1 in → 1 out8.5800 XPM116 B

AJCEY9yy…tg97E6zm

52ddf2fdb1bd7d…64e44860ca111b

1 in → 32 out78.5610 XPM1.22 KB

AUj1NbL2…nZT8UzfM AP8UXAGX…sg5Bdzmz AU5N7PqC…AqCAYzM4 AahNe9Eb…j7WvUkU7 AbBmufjy…bDwjMkmr

b5388e12ae98f5…86f61b09a1c008

1 in → 51 out50.7606 XPM1.85 KB

ALQG96NK…5zPi39NB AbqusThN…pNaPxYT2 Ad9ecvyC…zYhhDyAN AKSupGb1…qfxrLfcs ATF5aMuD…gKc7Tcff

7f670f5522e7b0…a88a29cb889e11

1 in → 51 out28.5902 XPM1.85 KB

AbkgeLEA…iFNYa3vD AaVTBaH5…XU1JJ57s AcmhVcUJ…JLTQEtJS AcJnL54o…nh1Ybi4A AKFPyFkJ…kHtmNvME

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.

1.902 × 10⁹⁶(97-digit number)

19022257542880401480…74437902443599298719

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

1.902 × 10⁹⁶(97-digit number)

19022257542880401480…74437902443599298719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.902 × 10⁹⁶(97-digit number)

19022257542880401480…74437902443599298721

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

3.804 × 10⁹⁶(97-digit number)

38044515085760802961…48875804887198597439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.804 × 10⁹⁶(97-digit number)

38044515085760802961…48875804887198597441

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

7.608 × 10⁹⁶(97-digit number)

76089030171521605923…97751609774397194879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.608 × 10⁹⁶(97-digit number)

76089030171521605923…97751609774397194881

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

1.521 × 10⁹⁷(98-digit number)

15217806034304321184…95503219548794389759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.521 × 10⁹⁷(98-digit number)

15217806034304321184…95503219548794389761

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

3.043 × 10⁹⁷(98-digit number)

30435612068608642369…91006439097588779519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.043 × 10⁹⁷(98-digit number)

30435612068608642369…91006439097588779521

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 #1,196,879

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