Block #276,069

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/27/2013, 12:19:32 AM · Difficulty 9.9623 · 6,532,814 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e37b699d78ec7c94d9aa1fb05f045aa9c829bb4b3c1afc6fb74a2bd48a7a301b

View on Chainz ↗

Height

#276,069

Difficulty

9.962310

Transactions

Size

1.15 KB

Version

Bits

09f659fb

Nonce

94,277

Timestamp

11/27/2013, 12:19:32 AM

Confirmations

6,532,814

Mined by

⛏️ e6aR:AY9F7ByyFafbT48koKkBBwvmVwEfAVw9Yf

Merkle Root

fffe66b41aa63f58f30bc026140bddafdd5331872a5769ff2f92d51c481bcc78

Transactions (1)

Coinbasefffe66b41aa63f…92d51c481bcc78

1 in → 30 out10.0400 XPM1.06 KB

AY9F7Byy…EfAVw9Yf Ac5sZcdP…kzV4eckG Ac7ndEyd…1EN9kFiR ARjgNH4d…BU7Drh7C AT5oTsET…Pi5H6raU

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.

2.456 × 10⁹⁹(100-digit number)

24564076387498921464…85059242157489999999

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

2.456 × 10⁹⁹(100-digit number)

24564076387498921464…85059242157489999999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.456 × 10⁹⁹(100-digit number)

24564076387498921464…85059242157490000001

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

4.912 × 10⁹⁹(100-digit number)

49128152774997842928…70118484314979999999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.912 × 10⁹⁹(100-digit number)

49128152774997842928…70118484314980000001

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

9.825 × 10⁹⁹(100-digit number)

98256305549995685856…40236968629959999999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.825 × 10⁹⁹(100-digit number)

98256305549995685856…40236968629960000001

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

1.965 × 10¹⁰⁰(101-digit number)

19651261109999137171…80473937259919999999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.965 × 10¹⁰⁰(101-digit number)

19651261109999137171…80473937259920000001

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

3.930 × 10¹⁰⁰(101-digit number)

39302522219998274342…60947874519839999999

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 #276,069

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