Block #457,564

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 3/23/2014, 11:57:17 PM · Difficulty 10.4202 · 6,335,270 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3cd3d3d7a35c813dc220edb8bd181b721e6aa70b47a4eacd2de9c8a52965dba3

View on Chainz ↗

Height

#457,564

Difficulty

10.420172

Transactions

Size

1.64 KB

Version

Bits

0a6b906a

Nonce

75,631

Timestamp

3/23/2014, 11:57:17 PM

Confirmations

6,335,270

Merkle Root

c27a894115deec469c098dd37bcb1a80715735d165e7e9e6f71f6dede616947d

Transactions (4)

Coinbase0247185ea33a47…6fdd64ab96ff15

1 in → 25 out9.2300 XPM913 B

AdFLJFhb…bsaVkAyh AH5mD99t…Spv1yg4N APtc8nU2…tp6qFHwW Adbb4svj…dQWTHsq5 AGz9gyZW…bo8NYQpw

a218dffdb25939…a7e1eb64f3de53

1 in → 2 out6.1537 XPM227 B

AbDBuYFj…Ys9qhQsE AFuiVYHe…FZJGkh32

be7ef69b638157…e8a88ad40b0b8c

1 in → 2 out2.2238 XPM225 B

AZLqmWPW…RugS55Li AdVv2jEK…aw4hyJCA

47d63238eb4ab1…6c1337c506db00

1 in → 2 out1.0872 XPM226 B

AbLDBWu5…wM6qdwfX AKDcdfep…ida8pdpd

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.

2.803 × 10⁹⁷(98-digit number)

28031824410740680459…75038590650352863999

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

2.803 × 10⁹⁷(98-digit number)

28031824410740680459…75038590650352863999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.803 × 10⁹⁷(98-digit number)

28031824410740680459…75038590650352864001

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

5.606 × 10⁹⁷(98-digit number)

56063648821481360919…50077181300705727999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.606 × 10⁹⁷(98-digit number)

56063648821481360919…50077181300705728001

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

1.121 × 10⁹⁸(99-digit number)

11212729764296272183…00154362601411455999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.121 × 10⁹⁸(99-digit number)

11212729764296272183…00154362601411456001

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

2.242 × 10⁹⁸(99-digit number)

22425459528592544367…00308725202822911999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.242 × 10⁹⁸(99-digit number)

22425459528592544367…00308725202822912001

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

4.485 × 10⁹⁸(99-digit number)

44850919057185088735…00617450405645823999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.485 × 10⁹⁸(99-digit number)

44850919057185088735…00617450405645824001

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

8.970 × 10⁹⁸(99-digit number)

89701838114370177471…01234900811291647999

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