Block #2,794,749

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 8/15/2018, 7:06:39 AM · Difficulty 11.6788 · 4,046,756 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

68c9e565068a416b6cffb4082166e7990593a0dfb8b531c76271394e57dac489

View on Chainz ↗

Height

#2,794,749

Difficulty

11.678773

Transactions

Size

1.80 KB

Version

Bits

0badc40c

Nonce

647,344,576

Timestamp

8/15/2018, 7:06:39 AM

Confirmations

4,046,756

Mined by

⛏️ P2SHAZtxQr2FMR4PURkVAAuK17mDJ17grUWrUz

Merkle Root

30843b99e521d8b6381a2197309cbc92fa24c938c59b3b89499e8bf767035557

Transactions (4)

Coinbase7087bae20a549a…b6b0fbf430c118

1 in → 1 out7.3500 XPM110 B

AZtxQr2F…7grUWrUz

19b120a04af2bd…2dda1151be1b05

4 in → 1 out8.0000 XPM603 B

ARezZb4y…FxP7ivbi

3632c8dc588706…52aaade64c4d87

3 in → 2 out4.4100 XPM522 B

AQsWqAY4…KRaKe7TG AH1sCwq4…fmhxWTBk

eabcce3e7c749b…3f1a04e8630875

3 in → 2 out4.0200 XPM520 B

AJ69hN3S…WJyH9SH3 AK1t5kps…i1QqwD8d

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.

1.985 × 10⁹⁷(98-digit number)

19859571208884647752…73218740121531023359

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

1.985 × 10⁹⁷(98-digit number)

19859571208884647752…73218740121531023359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.985 × 10⁹⁷(98-digit number)

19859571208884647752…73218740121531023361

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

3.971 × 10⁹⁷(98-digit number)

39719142417769295504…46437480243062046719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.971 × 10⁹⁷(98-digit number)

39719142417769295504…46437480243062046721

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

7.943 × 10⁹⁷(98-digit number)

79438284835538591009…92874960486124093439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.943 × 10⁹⁷(98-digit number)

79438284835538591009…92874960486124093441

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

1.588 × 10⁹⁸(99-digit number)

15887656967107718201…85749920972248186879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.588 × 10⁹⁸(99-digit number)

15887656967107718201…85749920972248186881

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

3.177 × 10⁹⁸(99-digit number)

31775313934215436403…71499841944496373759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.177 × 10⁹⁸(99-digit number)

31775313934215436403…71499841944496373761

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

6.355 × 10⁹⁸(99-digit number)

63550627868430872807…42999683888992747519

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 #2,794,749

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