Block #2,634,384

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 4/28/2018, 9:09:34 PM · Difficulty 11.2416 · 4,196,186 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2755480b2dc182bcf92a87e9bb72728566222e09ffa459a0e83ebeb900819dd8

View on Chainz ↗

Height

#2,634,384

Difficulty

11.241648

Transactions

Size

874 B

Version

Bits

0b3ddca8

Nonce

119,156,093

Timestamp

4/28/2018, 9:09:34 PM

Confirmations

4,196,186

Mined by

⛏️ P2SHAYPirZ5tFknhovDhBKLkhdDsWe66zAZhRz

Merkle Root

034e46b5bff5d81756046988c975d0ded39bee271a1fc5591ebe326fefc5cdef

Transactions (2)

Coinbase07ad8e025205e6…e99e63b44611ae

1 in → 1 out7.9100 XPM110 B

AYPirZ5t…66zAZhRz

f4b8e5d6495aec…bb2133a2abc5b3

4 in → 2 out11.0438 XPM673 B

AKyYvFp1…osuiJxTa AKCSvoxS…pqXFEBhu

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.

7.375 × 10⁹⁷(98-digit number)

73759720260812088570…64571077730011709439

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

7.375 × 10⁹⁷(98-digit number)

73759720260812088570…64571077730011709439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.375 × 10⁹⁷(98-digit number)

73759720260812088570…64571077730011709441

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

1.475 × 10⁹⁸(99-digit number)

14751944052162417714…29142155460023418879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.475 × 10⁹⁸(99-digit number)

14751944052162417714…29142155460023418881

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

2.950 × 10⁹⁸(99-digit number)

29503888104324835428…58284310920046837759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.950 × 10⁹⁸(99-digit number)

29503888104324835428…58284310920046837761

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

5.900 × 10⁹⁸(99-digit number)

59007776208649670856…16568621840093675519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.900 × 10⁹⁸(99-digit number)

59007776208649670856…16568621840093675521

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

1.180 × 10⁹⁹(100-digit number)

11801555241729934171…33137243680187351039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.180 × 10⁹⁹(100-digit number)

11801555241729934171…33137243680187351041

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

2.360 × 10⁹⁹(100-digit number)

23603110483459868342…66274487360374702079

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 #2,634,384

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