Block #1,947,342

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/20/2017, 11:28:54 PM · Difficulty 10.7291 · 4,870,532 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

029d034e15736a7c3d2f297846fb25d6d014791d33babbbc6489ddb7c96085d5

View on Chainz ↗

Height

#1,947,342

Difficulty

10.729127

Transactions

Size

2.94 KB

Version

Bits

0abaa80c

Nonce

191,369,718

Timestamp

1/20/2017, 11:28:54 PM

Confirmations

4,870,532

Mined by

⛏️ P2SHAafZ8tGydaEtHP6kYR3ksZP13vdnxmkFfz

Merkle Root

48bd591a10df766eedcf247c188ac672f06d3957015048181abd7138b55d24e7

Transactions (2)

Coinbase1da30b1fd49d56…a806023abe3bbb

1 in → 1 out8.7000 XPM109 B

AafZ8tGy…dnxmkFfz

8741684c50c81e…7e8e1244a2ff17

1 in → 78 out83.5203 XPM2.74 KB

ASQvdqX3…Kat24Gs9 Ab1hmXZp…mZYtBVXf AN4BEYbf…fwNE4V8q ARwiCsLc…t9tmA1LW ASUxZqk2…EZAU8DAt

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.

9.412 × 10⁹²(93-digit number)

94120943149623236710…10519244318276865189

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

9.412 × 10⁹²(93-digit number)

94120943149623236710…10519244318276865189

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.412 × 10⁹²(93-digit number)

94120943149623236710…10519244318276865191

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

1.882 × 10⁹³(94-digit number)

18824188629924647342…21038488636553730379

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.882 × 10⁹³(94-digit number)

18824188629924647342…21038488636553730381

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

3.764 × 10⁹³(94-digit number)

37648377259849294684…42076977273107460759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.764 × 10⁹³(94-digit number)

37648377259849294684…42076977273107460761

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

7.529 × 10⁹³(94-digit number)

75296754519698589368…84153954546214921519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.529 × 10⁹³(94-digit number)

75296754519698589368…84153954546214921521

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

1.505 × 10⁹⁴(95-digit number)

15059350903939717873…68307909092429843039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.505 × 10⁹⁴(95-digit number)

15059350903939717873…68307909092429843041

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

Block #1,947,342

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