Block #2,854,974

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 9/25/2018, 8:20:25 PM · Difficulty 11.7050 · 3,987,360 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c24bc7cfd52cdffb2680c43754050052a9883538391e54d8949b8ee3e4ec2321

View on Chainz ↗

Height

#2,854,974

Difficulty

11.704953

Transactions

Size

690 B

Version

Bits

0bb477d5

Nonce

577,167,481

Timestamp

9/25/2018, 8:20:25 PM

Confirmations

3,987,360

Mined by

⛏️ P2SHAUMQRepmQQz6L5K9d1Muaf8ABjtAfKmdW1

Merkle Root

54d632bedb33cbebad6d81515bb59d6aea24fa49de73319bbc7d6c03a7630f00

Transactions (2)

Coinbase533dfad3b7cc74…b192f19ae7d9c9

1 in → 1 out7.3000 XPM110 B

AUMQRepm…tAfKmdW1

c21b056104fe10…8e1d937cf9d128

3 in → 2 out10.7900 XPM489 B

ANWv5kFS…dkuSEoDi AadYtyde…FcTHpFKN

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.

1.517 × 10⁹⁷(98-digit number)

15171773759838876525…24168236920752793599

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

1.517 × 10⁹⁷(98-digit number)

15171773759838876525…24168236920752793599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.517 × 10⁹⁷(98-digit number)

15171773759838876525…24168236920752793601

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

3.034 × 10⁹⁷(98-digit number)

30343547519677753050…48336473841505587199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.034 × 10⁹⁷(98-digit number)

30343547519677753050…48336473841505587201

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

6.068 × 10⁹⁷(98-digit number)

60687095039355506100…96672947683011174399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.068 × 10⁹⁷(98-digit number)

60687095039355506100…96672947683011174401

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

1.213 × 10⁹⁸(99-digit number)

12137419007871101220…93345895366022348799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.213 × 10⁹⁸(99-digit number)

12137419007871101220…93345895366022348801

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

2.427 × 10⁹⁸(99-digit number)

24274838015742202440…86691790732044697599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.427 × 10⁹⁸(99-digit number)

24274838015742202440…86691790732044697601

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

4.854 × 10⁹⁸(99-digit number)

48549676031484404880…73383581464089395199

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 #2,854,974

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