Block #891,877

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/12/2015, 3:56:37 AM · Difficulty 10.9528 · 5,904,728 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a6a669f1f411c771fe24a4e718eabe81392b9ff6a96a3f7ed203f7f600b9cc9d

View on Chainz ↗

Height

#891,877

Difficulty

10.952843

Transactions

Size

1.08 KB

Version

Bits

0af3ed80

Nonce

646,260,112

Timestamp

1/12/2015, 3:56:37 AM

Confirmations

5,904,728

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

b0974e7fd374d3766b3a7506ab444bb4f003c085c8a11b35229b8fda159802ad

Transactions (3)

Coinbase1d29ca4dacb036…e9dc7666491a31

1 in → 1 out8.3400 XPM116 B

ANSXnLY2…Sd25TjkD

4457b168a3ed0b…f7edaf445de6b2

1 in → 2 out0.9851 XPM226 B

AFqpsntV…qebmi1Qk ALP6szJY…eEPSo5sX

0e7a02a98582f4…f0d4adc400bac3

4 in → 2 out0.6486 XPM673 B

Ad2xs189…XinUU69Y AHRoBSh4…BSVTQ36Q

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.

3.190 × 10⁹⁹(100-digit number)

31905769807746796265…67769022584279531519

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

3.190 × 10⁹⁹(100-digit number)

31905769807746796265…67769022584279531519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.190 × 10⁹⁹(100-digit number)

31905769807746796265…67769022584279531521

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

6.381 × 10⁹⁹(100-digit number)

63811539615493592530…35538045168559063039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.381 × 10⁹⁹(100-digit number)

63811539615493592530…35538045168559063041

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

1.276 × 10¹⁰⁰(101-digit number)

12762307923098718506…71076090337118126079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.276 × 10¹⁰⁰(101-digit number)

12762307923098718506…71076090337118126081

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

2.552 × 10¹⁰⁰(101-digit number)

25524615846197437012…42152180674236252159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.552 × 10¹⁰⁰(101-digit number)

25524615846197437012…42152180674236252161

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

5.104 × 10¹⁰⁰(101-digit number)

51049231692394874024…84304361348472504319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.104 × 10¹⁰⁰(101-digit number)

51049231692394874024…84304361348472504321

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