Block #2,653,758

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/8/2018, 4:38:33 PM · Difficulty 11.7327 · 4,176,966 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0a1116a3c69618dd6acc7c5501f27779ec59e54fb791522ff8e2f9a4334c0675

View on Chainz ↗

Height

#2,653,758

Difficulty

11.732672

Transactions

Size

425 B

Version

Bits

0bbb9060

Nonce

347,889,814

Timestamp

5/8/2018, 4:38:33 PM

Confirmations

4,176,966

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

a90aa62811de21b77a3f93169ce3b7e245aed48d92b97abecd47e2f51fe2a4b1

Transactions (2)

Coinbase3d5c02f4345fb1…3d2cff8ee7e73f

1 in → 1 out7.2600 XPM109 B

Adqah8zh…1WwoHJ9t

3bfc075db4b160…5e4f0de33e668f

1 in → 2 out1.0338 XPM227 B

AUrqu5L2…ZkgSBdjQ AHmoHaoV…guxDRZ3w

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.

1.226 × 10⁹²(93-digit number)

12265649248717645883…89506199505033953199

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

1.226 × 10⁹²(93-digit number)

12265649248717645883…89506199505033953199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.226 × 10⁹²(93-digit number)

12265649248717645883…89506199505033953201

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

2.453 × 10⁹²(93-digit number)

24531298497435291766…79012399010067906399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.453 × 10⁹²(93-digit number)

24531298497435291766…79012399010067906401

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

4.906 × 10⁹²(93-digit number)

49062596994870583533…58024798020135812799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.906 × 10⁹²(93-digit number)

49062596994870583533…58024798020135812801

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

9.812 × 10⁹²(93-digit number)

98125193989741167067…16049596040271625599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.812 × 10⁹²(93-digit number)

98125193989741167067…16049596040271625601

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

1.962 × 10⁹³(94-digit number)

19625038797948233413…32099192080543251199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.962 × 10⁹³(94-digit number)

19625038797948233413…32099192080543251201

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

3.925 × 10⁹³(94-digit number)

39250077595896466826…64198384161086502399

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 #2,653,758

Cookie Preferences