Block #2,716,521

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 6/22/2018, 2:11:31 PM · Difficulty 11.6137 · 4,120,623 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

fcd2bcfd66737e6ebe4deae421c454a99584021a8d1074138ddb5594d421eb74

View on Chainz ↗

Height

#2,716,521

Difficulty

11.613700

Transactions

Size

1.07 KB

Version

Bits

0b9d1b71

Nonce

734,113,298

Timestamp

6/22/2018, 2:11:31 PM

Confirmations

4,120,623

Mined by

⛏️ P2SHAX32fwtAiJyvgNgevDMn5aD2Sxi7hSzW4e

Merkle Root

5f334f137146ecbb130ee60b45a4024d6d531ea08991502809fa4aefa1e4c90c

Transactions (3)

Coinbase6e1ef5a2d101e6…a9e4f31285f497

1 in → 1 out7.4300 XPM110 B

AX32fwtA…i7hSzW4e

c46bf16e0a61a5…33e106317f7b53

3 in → 2 out1848.8435 XPM522 B

AVa5dYbR…j5uZYCvt AWy1c92U…vBKLJd77

d895faf47404b0…54fcb6ced36722

2 in → 2 out3.7957 XPM373 B

AbiZw7N1…HPacQJfk AW5rrGXU…rZk2pLW7

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.

1.918 × 10⁹⁴(95-digit number)

19181725392809670340…51779052683640322699

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

1.918 × 10⁹⁴(95-digit number)

19181725392809670340…51779052683640322699

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.918 × 10⁹⁴(95-digit number)

19181725392809670340…51779052683640322701

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

3.836 × 10⁹⁴(95-digit number)

38363450785619340681…03558105367280645399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.836 × 10⁹⁴(95-digit number)

38363450785619340681…03558105367280645401

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

7.672 × 10⁹⁴(95-digit number)

76726901571238681362…07116210734561290799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.672 × 10⁹⁴(95-digit number)

76726901571238681362…07116210734561290801

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

1.534 × 10⁹⁵(96-digit number)

15345380314247736272…14232421469122581599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.534 × 10⁹⁵(96-digit number)

15345380314247736272…14232421469122581601

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

3.069 × 10⁹⁵(96-digit number)

30690760628495472544…28464842938245163199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.069 × 10⁹⁵(96-digit number)

30690760628495472544…28464842938245163201

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

6.138 × 10⁹⁵(96-digit number)

61381521256990945089…56929685876490326399

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 #2,716,521

Cookie Preferences