Block #571,411

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 6/1/2014, 11:19:24 AM · Difficulty 10.9653 · 6,224,152 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a22662ea770151ce25eb07fa35aa77472af1b4b7599992191e10373555355c8f

View on Chainz ↗

Height

#571,411

Difficulty

10.965291

Transactions

Size

1.08 KB

Version

Bits

0af71d54

Nonce

192,229,429

Timestamp

6/1/2014, 11:19:24 AM

Confirmations

6,224,152

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

cbc6124eac13264cd6eafa7203f6c7a3a1e33d79cec93e12fc897b128a90605d

Transactions (5)

Coinbase8c667484511c7e…cb2864e3c3fa94

1 in → 1 out8.3400 XPM116 B

ANSXnLY2…Sd25TjkD

c5ec570c2b1cd4…75730af4ea1390

1 in → 2 out19.9995 XPM226 B

ARCQZsEz…xGp3QF1r AGBSWjaM…nRwmSLeo

0572057cd3c5f2…0101245046f680

1 in → 2 out7.7447 XPM226 B

AQw9971A…KY5NxdpK AHP6TNvX…4coFbeEa

c7e50e6984ca2d…fc7aa9c7e639a8

1 in → 2 out7.2778 XPM225 B

AJauqemE…5a989Avk AGpvdZiL…yRF55qor

a01f6b9e594250…568008d22de2ff

1 in → 2 out7.2751 XPM226 B

AJqybsFJ…DCGX1Cu3 ATxoEAVm…o1hPnNf4

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.

1.237 × 10⁹⁸(99-digit number)

12374617227536786857…14010941231955399999

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

1.237 × 10⁹⁸(99-digit number)

12374617227536786857…14010941231955399999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.237 × 10⁹⁸(99-digit number)

12374617227536786857…14010941231955400001

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

2.474 × 10⁹⁸(99-digit number)

24749234455073573715…28021882463910799999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.474 × 10⁹⁸(99-digit number)

24749234455073573715…28021882463910800001

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

4.949 × 10⁹⁸(99-digit number)

49498468910147147430…56043764927821599999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.949 × 10⁹⁸(99-digit number)

49498468910147147430…56043764927821600001

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

9.899 × 10⁹⁸(99-digit number)

98996937820294294861…12087529855643199999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.899 × 10⁹⁸(99-digit number)

98996937820294294861…12087529855643200001

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

1.979 × 10⁹⁹(100-digit number)

19799387564058858972…24175059711286399999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.979 × 10⁹⁹(100-digit number)

19799387564058858972…24175059711286400001

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

3.959 × 10⁹⁹(100-digit number)

39598775128117717944…48350119422572799999

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