Block #315,103

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/16/2013, 8:23:27 AM · Difficulty 10.0846 · 6,480,846 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9e04c5e42589d0a497c23b0708d2a6cd6b87c3e2fb4757c06bf0f0628630cebc

View on Chainz ↗

Height

#315,103

Difficulty

10.084568

Transactions

Size

11.40 KB

Version

Bits

0a15a644

Nonce

33,245

Timestamp

12/16/2013, 8:23:27 AM

Confirmations

6,480,846

Mined by

⛏️ P2SHAbfrYgdTZdsusJjXzjWiqxuMnyQxENkBYy

Merkle Root

9ed391165e8103ddafb3af0aafc72bd3a230771fbce1a61fb5e0b1b4ae9b9ee5

Transactions (2)

Coinbase6b91bd2e2b0e14…7a2915069b99ad

1 in → 1 out9.9400 XPM109 B

AbfrYgdT…QxENkBYy

a2ef276035a749…5115a328943cab

77 in → 2 out10000.0100 XPM11.20 KB

Ae5WFHbn…gBo7rvHr AT3h4qbJ…xJcbNJeh

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.

1.105 × 10¹⁰⁰(101-digit number)

11052479151715021095…96876911607738315519

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

1.105 × 10¹⁰⁰(101-digit number)

11052479151715021095…96876911607738315519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.105 × 10¹⁰⁰(101-digit number)

11052479151715021095…96876911607738315521

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

2.210 × 10¹⁰⁰(101-digit number)

22104958303430042191…93753823215476631039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.210 × 10¹⁰⁰(101-digit number)

22104958303430042191…93753823215476631041

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

4.420 × 10¹⁰⁰(101-digit number)

44209916606860084382…87507646430953262079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.420 × 10¹⁰⁰(101-digit number)

44209916606860084382…87507646430953262081

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

8.841 × 10¹⁰⁰(101-digit number)

88419833213720168764…75015292861906524159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.841 × 10¹⁰⁰(101-digit number)

88419833213720168764…75015292861906524161

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

1.768 × 10¹⁰¹(102-digit number)

17683966642744033752…50030585723813048319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.768 × 10¹⁰¹(102-digit number)

17683966642744033752…50030585723813048321

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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