Block #2,773,298

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 7/31/2018, 1:31:32 PM · Difficulty 11.6626 · 4,070,003 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c537efdaa26e925bb627183bb3fcda7c55fffa494158c719bef78473e2705b32

View on Chainz ↗

Height

#2,773,298

Difficulty

11.662625

Transactions

Size

880 B

Version

Bits

0ba9a1ce

Nonce

161,760,402

Timestamp

7/31/2018, 1:31:32 PM

Confirmations

4,070,003

Mined by

⛏️ P2SHAZtxQr2FMR4PURkVAAuK17mDJ17grUWrUz

Merkle Root

744bd30e26e6108fb981a230e52775764804ff544ec912560028d31d9ca31698

Transactions (4)

Coinbasee125a350916075…615ea807c86d0f

1 in → 1 out7.3700 XPM110 B

AZtxQr2F…7grUWrUz

50abc05f26e9a9…1c084f0472d42f

1 in → 2 out7.2097 XPM227 B

Aatwb5m5…CpUGXNMa AR84z5vH…Ro9Uy2zp

88fb3b8d6aff9d…a93bd094bfa33f

1 in → 2 out6.3000 XPM225 B

AMv64uDT…aEqYvY3e ALXs2nTW…DnYcDzFa

bf7be4845afd28…7a32ac2ac342d2

1 in → 2 out1.1352 XPM226 B

Aa1cbLt5…Nf58QkZT ARAgbBNg…NLYG6FgH

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.

1.166 × 10⁹⁹(100-digit number)

11662725809951941047…16668790553973882879

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

1.166 × 10⁹⁹(100-digit number)

11662725809951941047…16668790553973882879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.166 × 10⁹⁹(100-digit number)

11662725809951941047…16668790553973882881

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

2.332 × 10⁹⁹(100-digit number)

23325451619903882094…33337581107947765759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.332 × 10⁹⁹(100-digit number)

23325451619903882094…33337581107947765761

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

4.665 × 10⁹⁹(100-digit number)

46650903239807764188…66675162215895531519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.665 × 10⁹⁹(100-digit number)

46650903239807764188…66675162215895531521

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

9.330 × 10⁹⁹(100-digit number)

93301806479615528377…33350324431791063039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.330 × 10⁹⁹(100-digit number)

93301806479615528377…33350324431791063041

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

1.866 × 10¹⁰⁰(101-digit number)

18660361295923105675…66700648863582126079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.866 × 10¹⁰⁰(101-digit number)

18660361295923105675…66700648863582126081

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

3.732 × 10¹⁰⁰(101-digit number)

37320722591846211351…33401297727164252159

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 #2,773,298

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