Block #641,548

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 7/21/2014, 1:35:39 AM · Difficulty 10.9574 · 6,154,714 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

57410e679875acbfcc026fb94e0d14b52cad6c745392c377246a23fe1175eb76

View on Chainz ↗

Height

#641,548

Difficulty

10.957369

Transactions

Size

3.17 KB

Version

Bits

0af51625

Nonce

34,715,807

Timestamp

7/21/2014, 1:35:39 AM

Confirmations

6,154,714

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

f1cad61d983ba10782c06a0f678dc44fe5ad2e9fb4ca3a01e19d480083ecc8be

Transactions (3)

Coinbase7172ffb6e737dc…cd07d0f2ac1f8c

1 in → 1 out8.3600 XPM116 B

ANSXnLY2…Sd25TjkD

6e83f17412b08f…6fd575875331e3

15 in → 4 out6.0257 XPM2.32 KB

AMXQrWx5…XSxNgyAS AeKNrjNj…1NEq95Ta AcacZaAu…7XaX5VD6 AcADmAoe…8iNnoMzB

bb515cff22388e…f674cdb58640f9

4 in → 2 out5.1180 XPM671 B

ARpjHv1k…4F9NvuWN AWem786X…xEYAwwBM

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.

2.489 × 10⁹⁴(95-digit number)

24895368988336116098…28875669164192761459

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

2.489 × 10⁹⁴(95-digit number)

24895368988336116098…28875669164192761459

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.489 × 10⁹⁴(95-digit number)

24895368988336116098…28875669164192761461

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

4.979 × 10⁹⁴(95-digit number)

49790737976672232197…57751338328385522919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.979 × 10⁹⁴(95-digit number)

49790737976672232197…57751338328385522921

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

9.958 × 10⁹⁴(95-digit number)

99581475953344464394…15502676656771045839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.958 × 10⁹⁴(95-digit number)

99581475953344464394…15502676656771045841

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

1.991 × 10⁹⁵(96-digit number)

19916295190668892878…31005353313542091679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.991 × 10⁹⁵(96-digit number)

19916295190668892878…31005353313542091681

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

3.983 × 10⁹⁵(96-digit number)

39832590381337785757…62010706627084183359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.983 × 10⁹⁵(96-digit number)

39832590381337785757…62010706627084183361

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

7.966 × 10⁹⁵(96-digit number)

79665180762675571515…24021413254168366719

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