Block #2,665,926

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/17/2018, 10:47:10 PM · Difficulty 11.6639 · 4,166,756 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

506aa743955f8627e75544f2763795c684117f19c10038330f9f8c8ab9ef2ff8

View on Chainz ↗

Height

#2,665,926

Difficulty

11.663889

Transactions

Size

880 B

Version

Bits

0ba9f4a7

Nonce

1,790,973,024

Timestamp

5/17/2018, 10:47:10 PM

Confirmations

4,166,756

Mined by

⛏️ P2SHAecUmjdFuVkQSpRAkqqCrCrs66UpF82vhR

Merkle Root

f9a1133e8abc1b65dfa0816773496d07231c98dbcb952103f518a74789223407

Transactions (3)

Coinbase8ba0970894f918…8cf8b55727b9a9

1 in → 1 out7.3600 XPM110 B

AecUmjdF…UpF82vhR

cc4e1b8d4efc6f…dbde1453ca75f4

2 in → 2 out12.0800 XPM340 B

ANbEivYK…uHWztMaR AKfN5ELc…A3YNDXZ8

3cea537b8db485…fde64f579de422

2 in → 2 out12.0800 XPM339 B

AUKVmpkR…VaXGE8dX AW3QZZmg…j2rGjUkp

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.

3.086 × 10⁹⁶(97-digit number)

30863455351886015047…31578388434635541759

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

3.086 × 10⁹⁶(97-digit number)

30863455351886015047…31578388434635541759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.086 × 10⁹⁶(97-digit number)

30863455351886015047…31578388434635541761

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

6.172 × 10⁹⁶(97-digit number)

61726910703772030095…63156776869271083519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.172 × 10⁹⁶(97-digit number)

61726910703772030095…63156776869271083521

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

1.234 × 10⁹⁷(98-digit number)

12345382140754406019…26313553738542167039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.234 × 10⁹⁷(98-digit number)

12345382140754406019…26313553738542167041

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

2.469 × 10⁹⁷(98-digit number)

24690764281508812038…52627107477084334079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.469 × 10⁹⁷(98-digit number)

24690764281508812038…52627107477084334081

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

4.938 × 10⁹⁷(98-digit number)

49381528563017624076…05254214954168668159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.938 × 10⁹⁷(98-digit number)

49381528563017624076…05254214954168668161

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

9.876 × 10⁹⁷(98-digit number)

98763057126035248152…10508429908337336319

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 #2,665,926

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