Block #3,239,977

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 6/25/2019, 6:43:52 AM · Difficulty 10.9961 · 3,602,170 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9263ab54e55fdefaa487bdba542fce74d1e3cf7e1f3638e0c0218a800ff22f35

View on Chainz ↗

Height

#3,239,977

Difficulty

10.996094

Transactions

Size

1.27 KB

Version

Bits

0aff0000

Nonce

711,499,953

Timestamp

6/25/2019, 6:43:52 AM

Confirmations

3,602,170

Mined by

⛏️ P2SHARbm48qRsZyALB7gqdgsMMKGGA9xQc8DBX

Merkle Root

c290d9bf8558fefb72b3ce1da86217ef7f8b8740175af261eb46fabdeb135776

Transactions (5)

Coinbase59f8ca3822b81c…b5144338149513

1 in → 1 out8.3000 XPM110 B

ARbm48qR…9xQc8DBX

00c6c0e5363716…a97b01abe05b7b

1 in → 2 out8.2500 XPM193 B

AJtQNmM4…XBRjaQ6m ASiq2qtK…VMhmk7yL

d055404a8cb9bc…7385ea02c1bf4b

1 in → 1 out140.1049 XPM191 B

AXXGfizT…aeWx1Cui

1e2eca9b556506…2ffb4a95d55e03

3 in → 2 out15.8962 XPM488 B

AdGFnV3a…o6n2zX3x ASiq2qtK…VMhmk7yL

0097e129085cbd…776ee08651c2e1

1 in → 2 out1.1192 XPM225 B

ASiq2qtK…VMhmk7yL AQQ9ASfK…U13iNe1j

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.

4.958 × 10⁹⁶(97-digit number)

49589432160229821597…21414909132050559999

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

4.958 × 10⁹⁶(97-digit number)

49589432160229821597…21414909132050559999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.958 × 10⁹⁶(97-digit number)

49589432160229821597…21414909132050560001

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

9.917 × 10⁹⁶(97-digit number)

99178864320459643194…42829818264101119999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.917 × 10⁹⁶(97-digit number)

99178864320459643194…42829818264101120001

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

1.983 × 10⁹⁷(98-digit number)

19835772864091928638…85659636528202239999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.983 × 10⁹⁷(98-digit number)

19835772864091928638…85659636528202240001

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

3.967 × 10⁹⁷(98-digit number)

39671545728183857277…71319273056404479999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.967 × 10⁹⁷(98-digit number)

39671545728183857277…71319273056404480001

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

7.934 × 10⁹⁷(98-digit number)

79343091456367714555…42638546112808959999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.934 × 10⁹⁷(98-digit number)

79343091456367714555…42638546112808960001

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

1.586 × 10⁹⁸(99-digit number)

15868618291273542911…85277092225617919999

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #3,239,977

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