Block #2,783,871

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 8/7/2018, 9:14:37 PM · Difficulty 11.6651 · 4,058,123 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2e94c6032372e05005644d6a8117a9436dee3964cdafb3863ac4b2d57b3a111e

View on Chainz ↗

Height

#2,783,871

Difficulty

11.665127

Transactions

Size

1.30 KB

Version

Bits

0baa45c9

Nonce

2,083,772,915

Timestamp

8/7/2018, 9:14:37 PM

Confirmations

4,058,123

Mined by

⛏️ P2SHANGHgAqVJQLQ1K5mLdXA4X8jQ7oDP5mm5w

Merkle Root

14d0362304bef3813d0e182b274e580c913debd15fef1bcf086884b01f01d063

Transactions (4)

Coinbase4e38ca2152a520…be1653e978bd96

1 in → 1 out7.3700 XPM110 B

ANGHgAqV…oDP5mm5w

13f085d2a26f81…d70c8a6fb01cd6

1 in → 2 out7.3400 XPM192 B

AGLw31US…eBt9bzSV Aa1cbLt5…Nf58QkZT

6ad6a3e89aa395…25722266464c9c

3 in → 2 out21.0684 XPM454 B

AWddcU83…RSBKXbX6 AJX94Ph5…ZTjBYQwx

9a6d64a8e1a2de…2a4210d44f9224

3 in → 2 out10.6944 XPM488 B

AMePdneP…8NF3rHEh AbbzDU1H…t5xUiKdA

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.

1.320 × 10⁹⁹(100-digit number)

13206246630490912937…81806204981195571199

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

1.320 × 10⁹⁹(100-digit number)

13206246630490912937…81806204981195571199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.320 × 10⁹⁹(100-digit number)

13206246630490912937…81806204981195571201

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

2.641 × 10⁹⁹(100-digit number)

26412493260981825875…63612409962391142399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.641 × 10⁹⁹(100-digit number)

26412493260981825875…63612409962391142401

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

5.282 × 10⁹⁹(100-digit number)

52824986521963651751…27224819924782284799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.282 × 10⁹⁹(100-digit number)

52824986521963651751…27224819924782284801

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

1.056 × 10¹⁰⁰(101-digit number)

10564997304392730350…54449639849564569599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.056 × 10¹⁰⁰(101-digit number)

10564997304392730350…54449639849564569601

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

2.112 × 10¹⁰⁰(101-digit number)

21129994608785460700…08899279699129139199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.112 × 10¹⁰⁰(101-digit number)

21129994608785460700…08899279699129139201

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

4.225 × 10¹⁰⁰(101-digit number)

42259989217570921401…17798559398258278399

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 #2,783,871

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