Block #571,333

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 6/1/2014, 10:06:32 AM · Difficulty 10.9652 · 6,238,477 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

01c03a82d2d5788623a7aaa8510c125db6f06e30d51d014e14649e343603cc42

View on Chainz ↗

Height

#571,333

Difficulty

10.965249

Transactions

Size

1.86 KB

Version

Bits

0af71a94

Nonce

150

Timestamp

6/1/2014, 10:06:32 AM

Confirmations

6,238,477

Mined by

⛏️ aS8!AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

70b157a5195a72d6ef98d9c73873e51c42f3c20e74ecf797d318501ee52c712d

Transactions (4)

Coinbased3d3fd238bc308…067e7c4a3d8aa9

1 in → 13 out8.3000 XPM505 B

AQvZBsUo…hppgRZTJ AJzWx2VD…j4ZSMit5 AJtNW28X…Syb4Ph5j AdxPNkWD…ZMa9u34q AQyr8Lw3…hs4nt3Pn

38929ad2d7f8c8…fcb0243862da0a

2 in → 2 out10.3364 XPM376 B

AVH54nHM…1mb6Xvbn AZasRLps…qVSdTCis

06d30d70de3bdf…9395d620406cfb

4 in → 4 out9.1347 XPM705 B

AeKNrjNj…1NEq95Ta ANduR3jU…CEMsRF97 AHy24nCY…4KpVC1Hz AFtKUKUa…WyLEn4xB

36c2bd97463be3…41acccd492a97a

1 in → 2 out7.7747 XPM225 B

AKams3Bw…coWAzP91 AJbxxT8R…gBxqX66F

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.

8.861 × 10⁹¹(92-digit number)

88614488596040939651…54750573114252679679

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

8.861 × 10⁹¹(92-digit number)

88614488596040939651…54750573114252679679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.861 × 10⁹¹(92-digit number)

88614488596040939651…54750573114252679681

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

1.772 × 10⁹²(93-digit number)

17722897719208187930…09501146228505359359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.772 × 10⁹²(93-digit number)

17722897719208187930…09501146228505359361

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

3.544 × 10⁹²(93-digit number)

35445795438416375860…19002292457010718719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.544 × 10⁹²(93-digit number)

35445795438416375860…19002292457010718721

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

7.089 × 10⁹²(93-digit number)

70891590876832751721…38004584914021437439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.089 × 10⁹²(93-digit number)

70891590876832751721…38004584914021437441

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

1.417 × 10⁹³(94-digit number)

14178318175366550344…76009169828042874879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.417 × 10⁹³(94-digit number)

14178318175366550344…76009169828042874881

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

2.835 × 10⁹³(94-digit number)

28356636350733100688…52018339656085749759

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 #571,333

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