Block #2,880,708

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 10/14/2018, 12:01:30 PM · Difficulty 11.6319 · 3,958,131 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

fb812e42a3267d048d6588e7cbb6e30e828f4150fd9503a2f3e4d6e171292f1d

View on Chainz ↗

Height

#2,880,708

Difficulty

11.631945

Transactions

Size

3.16 KB

Version

Bits

0ba1c728

Nonce

167,859,534

Timestamp

10/14/2018, 12:01:30 PM

Confirmations

3,958,131

Mined by

⛏️ P2SHAbM2mvjx8qfSHArxd1wKmEvKC4jcC7mMQT

Merkle Root

b0d102eb2cef66510b22ea216fa706b86cd74e43db156527f16ea7127ed05f3d

Transactions (4)

Coinbase799ef42b8883d3…20dc1782a851fd

1 in → 1 out7.4300 XPM110 B

AbM2mvjx…jcC7mMQT

2d101ba3cbba50…4b0600b84c7a9e

21 in → 2 out120.0408 XPM2.58 KB

AbaTUvwE…k8FVujZz AKDVWTfJ…cs61LfXo

18cfed1f64e121…865e056667540c

1 in → 2 out7.3500 XPM192 B

AdoL6hKY…3zjRyHhC Ac9uogni…KtQzAqJt

1cf1d26981c80b…ddf29c5ede34fd

1 in → 2 out7.3500 XPM193 B

AXGyihky…F4qD8E72 AMDrVCQK…CyujWz2r

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.

1.086 × 10⁹⁹(100-digit number)

10864811631977127013…68819284847124807679

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

1.086 × 10⁹⁹(100-digit number)

10864811631977127013…68819284847124807679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.086 × 10⁹⁹(100-digit number)

10864811631977127013…68819284847124807681

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

2.172 × 10⁹⁹(100-digit number)

21729623263954254026…37638569694249615359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.172 × 10⁹⁹(100-digit number)

21729623263954254026…37638569694249615361

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

4.345 × 10⁹⁹(100-digit number)

43459246527908508052…75277139388499230719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.345 × 10⁹⁹(100-digit number)

43459246527908508052…75277139388499230721

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

8.691 × 10⁹⁹(100-digit number)

86918493055817016105…50554278776998461439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.691 × 10⁹⁹(100-digit number)

86918493055817016105…50554278776998461441

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

1.738 × 10¹⁰⁰(101-digit number)

17383698611163403221…01108557553996922879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.738 × 10¹⁰⁰(101-digit number)

17383698611163403221…01108557553996922881

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

3.476 × 10¹⁰⁰(101-digit number)

34767397222326806442…02217115107993845759

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 #2,880,708

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