Block #2,679,076

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/26/2018, 6:24:41 PM · Difficulty 11.6932 · 4,151,956 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e8fd495c48a6f5e8adc3ded64ee8c05c7dc35cf13634ee245506316f8e1ed386

View on Chainz ↗

Height

#2,679,076

Difficulty

11.693155

Transactions

Size

1.72 KB

Version

Bits

0bb17295

Nonce

665,490,302

Timestamp

5/26/2018, 6:24:41 PM

Confirmations

4,151,956

Mined by

⛏️ P2SHALWMBEVxQMQKH2twvBdQtWkUHBHbZmpxcv

Merkle Root

f2a1fe85b49e76cdd212771cf6f059e48504a63e478f5a611018ab55b3eb22c2

Transactions (4)

Coinbaseee8facac987a57…fd6362dd5918f1

1 in → 1 out7.3300 XPM110 B

ALWMBEVx…HbZmpxcv

c0e39e7a11134b…109e7699a5ad68

3 in → 2 out858.8000 XPM522 B

AYNVicgy…BqwF4WMQ AKf74TEF…iNryuktP

2177aecb1d70f1…5a87df95aa1267

4 in → 2 out4.1171 XPM670 B

AKWVcUGA…hkT81NSY AZ4UnHzJ…PH7NQioA

0b98d8e77b04af…0178b11fc5bbf8

2 in → 2 out4.2705 XPM374 B

AaZpjAJg…qRCoEDsy ALFCjDjB…XEfXtzaq

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.

1.240 × 10⁹⁵(96-digit number)

12409626710625692377…40804691820888444479

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

1.240 × 10⁹⁵(96-digit number)

12409626710625692377…40804691820888444479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.240 × 10⁹⁵(96-digit number)

12409626710625692377…40804691820888444481

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

2.481 × 10⁹⁵(96-digit number)

24819253421251384754…81609383641776888959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.481 × 10⁹⁵(96-digit number)

24819253421251384754…81609383641776888961

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

4.963 × 10⁹⁵(96-digit number)

49638506842502769508…63218767283553777919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.963 × 10⁹⁵(96-digit number)

49638506842502769508…63218767283553777921

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

9.927 × 10⁹⁵(96-digit number)

99277013685005539016…26437534567107555839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.927 × 10⁹⁵(96-digit number)

99277013685005539016…26437534567107555841

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

1.985 × 10⁹⁶(97-digit number)

19855402737001107803…52875069134215111679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.985 × 10⁹⁶(97-digit number)

19855402737001107803…52875069134215111681

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

3.971 × 10⁹⁶(97-digit number)

39710805474002215606…05750138268430223359

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 #2,679,076

Cookie Preferences