Block #2,695,723

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 6/7/2018, 1:13:38 PM · Difficulty 11.6736 · 4,137,366 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b325ac9817043f6244094a9ccd3d10003906bd0d61a95e7bc57d9a5094af9562

View on Chainz ↗

Height

#2,695,723

Difficulty

11.673563

Transactions

Size

1.30 KB

Version

Bits

0bac6e9e

Nonce

698,948,604

Timestamp

6/7/2018, 1:13:38 PM

Confirmations

4,137,366

Mined by

⛏️ P2SHANJNfNumgCK4AnZEeDHgtvxhtUg5Sex3oK

Merkle Root

eda51e2a0cfbdb2033b166af87771af71e73b8ba5e8e00f021960437e2d33bc5

Transactions (4)

Coinbaseef65ec0d9850db…6ff594fc91cbb3

1 in → 1 out7.3600 XPM109 B

ANJNfNum…g5Sex3oK

868404f295d9c1…62ff98cf902e99

2 in → 2 out14.6400 XPM306 B

AbgkRZKt…VcCH28UZ AankNErj…v4An9BCh

fc3be256f3209f…e68f6d366c921f

2 in → 2 out14.6100 XPM306 B

Aei7Ymdr…MjKXcgCp AYwraL7y…YDUFmj3s

8a78a7c1141196…a8cf981823e4db

3 in → 2 out10.3500 XPM522 B

AHGdMwSS…ptao1h8e AW3QZZmg…j2rGjUkp

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.

1.819 × 10⁹⁶(97-digit number)

18190920648876380616…66226286749539532799

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

1.819 × 10⁹⁶(97-digit number)

18190920648876380616…66226286749539532799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.819 × 10⁹⁶(97-digit number)

18190920648876380616…66226286749539532801

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

3.638 × 10⁹⁶(97-digit number)

36381841297752761233…32452573499079065599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.638 × 10⁹⁶(97-digit number)

36381841297752761233…32452573499079065601

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

7.276 × 10⁹⁶(97-digit number)

72763682595505522466…64905146998158131199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.276 × 10⁹⁶(97-digit number)

72763682595505522466…64905146998158131201

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

1.455 × 10⁹⁷(98-digit number)

14552736519101104493…29810293996316262399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.455 × 10⁹⁷(98-digit number)

14552736519101104493…29810293996316262401

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

2.910 × 10⁹⁷(98-digit number)

29105473038202208986…59620587992632524799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.910 × 10⁹⁷(98-digit number)

29105473038202208986…59620587992632524801

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

5.821 × 10⁹⁷(98-digit number)

58210946076404417972…19241175985265049599

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 #2,695,723

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