Block #2,727,444

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 6/30/2018, 1:34:00 AM · Difficulty 11.6263 · 4,111,908 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

86d77c58e452a8bd98071c2c2e9553574d07e0d67151b91d1664c9320d600994

View on Chainz ↗

Height

#2,727,444

Difficulty

11.626252

Transactions

Size

1.00 KB

Version

Bits

0ba05214

Nonce

633,211,146

Timestamp

6/30/2018, 1:34:00 AM

Confirmations

4,111,908

Mined by

⛏️ P2SHANLc3RDrNRtEozSbcgTnJ36EpjiYSoA2Td

Merkle Root

076efe1bbb90a6bf748b37de04cfc9e1c96730977a2725976f4e18f7a1f8a3e0

Transactions (3)

Coinbased68f93655697fb…54ca07a265f716

1 in → 1 out7.4100 XPM109 B

ANLc3RDr…iYSoA2Td

a0efe145b7e8b6…f9ecc3b439f145

2 in → 2 out12.2100 XPM341 B

ANccuwPh…TvQU6SpC AcXtoaKv…4oXYPT9v

7ae10f1898202b…b1f83a65089b6e

3 in → 2 out11.7600 XPM489 B

Acif2TJg…eKiurkod APVKWthF…PMMxwRoz

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.

1.393 × 10⁹⁴(95-digit number)

13938853244702757225…06969384707934728959

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

1.393 × 10⁹⁴(95-digit number)

13938853244702757225…06969384707934728959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.393 × 10⁹⁴(95-digit number)

13938853244702757225…06969384707934728961

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

2.787 × 10⁹⁴(95-digit number)

27877706489405514451…13938769415869457919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.787 × 10⁹⁴(95-digit number)

27877706489405514451…13938769415869457921

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

5.575 × 10⁹⁴(95-digit number)

55755412978811028903…27877538831738915839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.575 × 10⁹⁴(95-digit number)

55755412978811028903…27877538831738915841

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

1.115 × 10⁹⁵(96-digit number)

11151082595762205780…55755077663477831679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.115 × 10⁹⁵(96-digit number)

11151082595762205780…55755077663477831681

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

2.230 × 10⁹⁵(96-digit number)

22302165191524411561…11510155326955663359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.230 × 10⁹⁵(96-digit number)

22302165191524411561…11510155326955663361

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

4.460 × 10⁹⁵(96-digit number)

44604330383048823122…23020310653911326719

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 #2,727,444

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