Block #2,633,092

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 4/28/2018, 6:43:00 AM · Difficulty 11.1753 · 4,211,347 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

28151e62b3239c37d8db352d07f3093f2fe49160f8add160391e98ea0072be70

View on Chainz ↗

Height

#2,633,092

Difficulty

11.175292

Transactions

Size

15.60 KB

Version

Bits

0b2cdfef

Nonce

1,893,610,465

Timestamp

4/28/2018, 6:43:00 AM

Confirmations

4,211,347

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

ff51e17cf4f31784a56c5cf44c6b5eaa114f940dbe8b66ef2bab544f064d510f

Transactions (4)

Coinbase6c6a514a673e8b…678168d08641e6

1 in → 1 out8.1700 XPM110 B

Adqah8zh…1WwoHJ9t

63b8f7eab209b9…8190fd819a08d1

2 in → 2 out813.2156 XPM374 B

AaKZGoM6…w6VRC6uK ALYePk6J…7ZENAizD

6ed3660735c928…d60c13aac4f3e9

101 in → 2 out1000.8300 XPM14.67 KB

AKPH6BPo…grBFmzZk ATkpsqKM…mmLKcTze

74422ca6bffa2c…4f070567563c13

2 in → 2 out3.9146 XPM375 B

AHLPUwXV…p1Q6Denj AXnWN4rQ…DYMFt1eB

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.

2.008 × 10⁹⁵(96-digit number)

20083752221900390213…32127660798182043999

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

2.008 × 10⁹⁵(96-digit number)

20083752221900390213…32127660798182043999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.008 × 10⁹⁵(96-digit number)

20083752221900390213…32127660798182044001

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

4.016 × 10⁹⁵(96-digit number)

40167504443800780427…64255321596364087999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.016 × 10⁹⁵(96-digit number)

40167504443800780427…64255321596364088001

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

8.033 × 10⁹⁵(96-digit number)

80335008887601560854…28510643192728175999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.033 × 10⁹⁵(96-digit number)

80335008887601560854…28510643192728176001

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

1.606 × 10⁹⁶(97-digit number)

16067001777520312170…57021286385456351999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.606 × 10⁹⁶(97-digit number)

16067001777520312170…57021286385456352001

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

3.213 × 10⁹⁶(97-digit number)

32134003555040624341…14042572770912703999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.213 × 10⁹⁶(97-digit number)

32134003555040624341…14042572770912704001

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

6.426 × 10⁹⁶(97-digit number)

64268007110081248683…28085145541825407999

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 #2,633,092

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