Block #470,411

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/1/2014, 9:17:43 PM · Difficulty 10.4330 · 6,340,095 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

24e9f6dd76487bda2374cbd07c5fda51ee0c51d72b51f80ad274a62a71976a54

View on Chainz ↗

Height

#470,411

Difficulty

10.433038

Transactions

Size

1.73 KB

Version

Bits

0a6edb91

Nonce

147,349

Timestamp

4/1/2014, 9:17:43 PM

Confirmations

6,340,095

Mined by

⛏️ -UAMVf7JrgD9LEuSS2R27DgQAdb3xd5AVR7C

Merkle Root

70ac021e63e88f0e9dbea305001d51b8db3a9a7f52559f31cc0eb1e9a36efa64

Transactions (5)

Coinbase0d72a3add30223…5ff694a3f84375

1 in → 3 out9.2200 XPM165 B

AMVf7Jrg…xd5AVR7C ALzzzbUz…2Cb4jSDN AJno7LX2…vo4wdWtY

5e49ff92ade24c…71d79cd1f4fc77

4 in → 10 out28.3723 XPM842 B

AXSSYByb…8vG2sYWV AHy24nCY…4KpVC1Hz AWWeSvQW…Vm84TjJn AU328Zva…1UF3tiZF ANt8CsTm…XxNi34u4

a91a0853561bda…c57e5d967db109

1 in → 2 out5.6048 XPM227 B

Ad2MVWji…27cgMffG Ab4vvZZW…RRE1UAQ8

a4ba1b7f436d4f…cd8b5b6a9abacf

1 in → 2 out2.5242 XPM225 B

AZ6mcbMN…TgjsrbsR AXPjDsq5…ep9XQVRb

b817b9804ee7f1…098566be1ce8fe

1 in → 2 out4.6034 XPM226 B

ARvKqoef…XiRLShTw AGoNi5MG…ZDc5F7vQ

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.

7.953 × 10⁹⁴(95-digit number)

79535353265020747390…23695548046688539759

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

7.953 × 10⁹⁴(95-digit number)

79535353265020747390…23695548046688539759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.953 × 10⁹⁴(95-digit number)

79535353265020747390…23695548046688539761

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

1.590 × 10⁹⁵(96-digit number)

15907070653004149478…47391096093377079519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.590 × 10⁹⁵(96-digit number)

15907070653004149478…47391096093377079521

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

3.181 × 10⁹⁵(96-digit number)

31814141306008298956…94782192186754159039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.181 × 10⁹⁵(96-digit number)

31814141306008298956…94782192186754159041

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

6.362 × 10⁹⁵(96-digit number)

63628282612016597912…89564384373508318079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.362 × 10⁹⁵(96-digit number)

63628282612016597912…89564384373508318081

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

1.272 × 10⁹⁶(97-digit number)

12725656522403319582…79128768747016636159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.272 × 10⁹⁶(97-digit number)

12725656522403319582…79128768747016636161

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #470,411

Cookie Preferences