Block #2,758,711

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 7/21/2018, 9:30:10 AM · Difficulty 11.6659 · 4,078,080 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

547637a402f57484a77ef6209e435c18de686a1093b7a280a179c795a9acdfad

View on Chainz ↗

Height

#2,758,711

Difficulty

11.665868

Transactions

Size

1.30 KB

Version

Bits

0baa7651

Nonce

1,931,664,039

Timestamp

7/21/2018, 9:30:10 AM

Confirmations

4,078,080

Mined by

⛏️ P2SHAZtxQr2FMR4PURkVAAuK17mDJ17grUWrUz

Merkle Root

014cf2990b910368b3422aa998e62370f955a35fa7a8a968d37bf8471695362b

Transactions (4)

Coinbase3e8a5536dd4035…bb153b402fc25c

1 in → 1 out7.3700 XPM110 B

AZtxQr2F…7grUWrUz

e62e6ce81f5a70…14c1db9022eaa3

5 in → 2 out32.3820 XPM683 B

ALzB5ZBV…7snFdEnf ANz65jvR…vu7Ymacm

67e9e3501cdded…163a84e20c8d8c

1 in → 2 out4.6760 XPM226 B

AZqy5MQF…7NUd22pZ AdGFnV3a…o6n2zX3x

c8ef35ea0791b8…6e4e623789995b

1 in → 2 out3.2790 XPM227 B

AepyHUmx…QYcCRqK4 Ad9DPQy8…7LY8jjYB

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.

1.505 × 10⁹²(93-digit number)

15059974330446678222…64444191224204158969

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

1.505 × 10⁹²(93-digit number)

15059974330446678222…64444191224204158969

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.505 × 10⁹²(93-digit number)

15059974330446678222…64444191224204158971

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

3.011 × 10⁹²(93-digit number)

30119948660893356445…28888382448408317939

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.011 × 10⁹²(93-digit number)

30119948660893356445…28888382448408317941

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

6.023 × 10⁹²(93-digit number)

60239897321786712890…57776764896816635879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.023 × 10⁹²(93-digit number)

60239897321786712890…57776764896816635881

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

1.204 × 10⁹³(94-digit number)

12047979464357342578…15553529793633271759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.204 × 10⁹³(94-digit number)

12047979464357342578…15553529793633271761

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

2.409 × 10⁹³(94-digit number)

24095958928714685156…31107059587266543519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.409 × 10⁹³(94-digit number)

24095958928714685156…31107059587266543521

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

4.819 × 10⁹³(94-digit number)

48191917857429370312…62214119174533087039

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 #2,758,711

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