Block #2,786,785

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 8/9/2018, 7:49:29 PM · Difficulty 11.6732 · 4,052,035 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f597b724281495faf9ea4917baf45315d549b9ece333ac8060807abe17f43065

View on Chainz ↗

Height

#2,786,785

Difficulty

11.673230

Transactions

Size

1.96 KB

Version

Bits

0bac58d5

Nonce

651,926,836

Timestamp

8/9/2018, 7:49:29 PM

Confirmations

4,052,035

Mined by

⛏️ P2SHAZtxQr2FMR4PURkVAAuK17mDJ17grUWrUz

Merkle Root

85423e8c723250d35d99bea5cacaf3990f55559cbebd09536350af7d82e8ba4c

Transactions (5)

Coinbase66f060a9540414…ff60d98ce850a2

1 in → 1 out7.3700 XPM110 B

AZtxQr2F…7grUWrUz

974c003086109e…a943fd8e1b48f3

4 in → 2 out127.8796 XPM669 B

AGWpR3uq…5xNaaR9k AWNra1VM…ag3dXg14

77b4f056d8e58d…064d88ec3588a4

2 in → 2 out14.6700 XPM307 B

AW3QZZmg…j2rGjUkp AbEHf1FK…vp2mfj4g

d43c454de72b13…f138ec90a51465

2 in → 2 out12.0000 XPM340 B

AM7HYByC…YhcyJvAq AJARC7ma…VgmXXXLQ

f235cfd397b64d…11004ac997d411

3 in → 2 out10.6700 XPM488 B

AaqK6FAd…b3sjMQ3E AKsVW9LP…HrbLzAf4

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.

1.268 × 10⁹⁴(95-digit number)

12682377943860710916…56624623247766846719

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

1.268 × 10⁹⁴(95-digit number)

12682377943860710916…56624623247766846719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.268 × 10⁹⁴(95-digit number)

12682377943860710916…56624623247766846721

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

2.536 × 10⁹⁴(95-digit number)

25364755887721421833…13249246495533693439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.536 × 10⁹⁴(95-digit number)

25364755887721421833…13249246495533693441

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

5.072 × 10⁹⁴(95-digit number)

50729511775442843667…26498492991067386879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.072 × 10⁹⁴(95-digit number)

50729511775442843667…26498492991067386881

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

1.014 × 10⁹⁵(96-digit number)

10145902355088568733…52996985982134773759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.014 × 10⁹⁵(96-digit number)

10145902355088568733…52996985982134773761

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

2.029 × 10⁹⁵(96-digit number)

20291804710177137466…05993971964269547519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.029 × 10⁹⁵(96-digit number)

20291804710177137466…05993971964269547521

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

4.058 × 10⁹⁵(96-digit number)

40583609420354274933…11987943928539095039

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 #2,786,785

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