Block #275,164

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/26/2013, 2:17:48 PM · Difficulty 9.9599 · 6,520,746 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

bbbe1c93867eeb871ea702119ee2f0b6d565036172322a53102a63a59978a217

View on Chainz ↗

Height

#275,164

Difficulty

9.959946

Transactions

Size

2.11 KB

Version

Bits

09f5bf0c

Nonce

2,520

Timestamp

11/26/2013, 2:17:48 PM

Confirmations

6,520,746

Mined by

⛏️ P2SHAKcbk49N7DP3nse7MJr3Ed6rZiGJbKa7j1

Merkle Root

ef451513313fd07703f100acb327893077e58cd7a6a8e6a31aa6857434a8c3c3

Transactions (3)

Coinbasec4c5ea508a7549…59db724bcd1bfd

1 in → 2 out10.1000 XPM141 B

AKcbk49N…GJbKa7j1 AHsw4d6U…EnM8UXNZ

226fde74be14a8…af58cb6a3c2f2e

2 in → 2 out2.5702 XPM374 B

ANGhYCRV…QumSTgZu AWkxEq8A…Ai2hZNhN

d1170f542796b6…0bd54521cc1949

10 in → 2 out94.0105 XPM1.52 KB

AK58VXYn…2Yr6Zd6k AcEUjB8T…7y8mLUDZ

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.

8.491 × 10¹⁰³(104-digit number)

84910506677061482036…75188418297602904959

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

8.491 × 10¹⁰³(104-digit number)

84910506677061482036…75188418297602904959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.491 × 10¹⁰³(104-digit number)

84910506677061482036…75188418297602904961

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

1.698 × 10¹⁰⁴(105-digit number)

16982101335412296407…50376836595205809919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.698 × 10¹⁰⁴(105-digit number)

16982101335412296407…50376836595205809921

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

3.396 × 10¹⁰⁴(105-digit number)

33964202670824592814…00753673190411619839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.396 × 10¹⁰⁴(105-digit number)

33964202670824592814…00753673190411619841

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

6.792 × 10¹⁰⁴(105-digit number)

67928405341649185629…01507346380823239679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.792 × 10¹⁰⁴(105-digit number)

67928405341649185629…01507346380823239681

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

1.358 × 10¹⁰⁵(106-digit number)

13585681068329837125…03014692761646479359

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