Block #2,653,384

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/8/2018, 8:49:51 AM · Difficulty 11.7376 · 4,187,748 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9cf99a6d9f1af57a80eb52e6c5df6fe84f5a955b11f57c3256bbce12088f91f9

View on Chainz ↗

Height

#2,653,384

Difficulty

11.737628

Transactions

Size

1.14 KB

Version

Bits

0bbcd531

Nonce

87,937,717

Timestamp

5/8/2018, 8:49:51 AM

Confirmations

4,187,748

Mined by

⛏️ P2SHAcsM4pjhckWHDRuq77SH5S2yZ4X45B7TDi

Merkle Root

ce50700ed4e06cb9a9be70ffe9d6314fad5e051789053d34a4fbfa6ae0765450

Transactions (2)

Coinbase1ea0e22fe77630…5cda877c4f414c

1 in → 1 out7.2600 XPM110 B

AcsM4pjh…X45B7TDi

1a7d3e8788eb66…f59d43a1f3951e

6 in → 2 out820.3193 XPM967 B

AFzTU49M…RvzgfQtw ATLw4wqX…kGTEjXFm

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.

1.485 × 10⁹⁶(97-digit number)

14855611403989147761…92854916798198983679

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

1.485 × 10⁹⁶(97-digit number)

14855611403989147761…92854916798198983679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.485 × 10⁹⁶(97-digit number)

14855611403989147761…92854916798198983681

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

2.971 × 10⁹⁶(97-digit number)

29711222807978295523…85709833596397967359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.971 × 10⁹⁶(97-digit number)

29711222807978295523…85709833596397967361

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

5.942 × 10⁹⁶(97-digit number)

59422445615956591047…71419667192795934719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.942 × 10⁹⁶(97-digit number)

59422445615956591047…71419667192795934721

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

1.188 × 10⁹⁷(98-digit number)

11884489123191318209…42839334385591869439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.188 × 10⁹⁷(98-digit number)

11884489123191318209…42839334385591869441

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

2.376 × 10⁹⁷(98-digit number)

23768978246382636418…85678668771183738879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.376 × 10⁹⁷(98-digit number)

23768978246382636418…85678668771183738881

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

4.753 × 10⁹⁷(98-digit number)

47537956492765272837…71357337542367477759

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 #2,653,384

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