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Block #480,624

TWNLength 10ā˜…ā˜…ā˜†ā˜†ā˜†

Bi-Twin Chain Ā· Discovered 4/8/2014, 10:23:35 AM Ā· Difficulty 10.5188 Ā· 6,315,664 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
d424c23fd7ff7d3282e0a8a1a710b7cc7570427a010ee31408e8e9a15b2ef3c3
View on Chainz ā†—

Height

#480,624

Difficulty

10.518752

Transactions

5

Size

1.48 KB

Version

2

Bits

0a84ccf1

Nonce

11,794,213

Timestamp

4/8/2014, 10:23:35 AM

Confirmations

6,315,664

Mined by

ā›ļø P2SHAbg4BYbkV6AP6isnq8hoV45xE5drFWetJq

Merkle Root

7aa269520afd08a6dfb355741696fd4fa8e539f85df799c354d6aa726d9dfd7d
Transactions (5)
Coinbase3e8d73cd006701ā€¦07b49360198110
1 in ā†’ 1 out9.0611 XPM110 B
Abg4BYbkā€¦drFWetJq
2664e82e6a440cā€¦11f93bfb32a414
4 in ā†’ 1 out3.4400 XPM638 B
AHH947Pxā€¦jVKVNB1m
05257825e3e73dā€¦c9bcaf569cf3b5
1 in ā†’ 2 out7.5545 XPM225 B
AXmtodsnā€¦45BD8zrNAPeSqA6Rā€¦nCeekPkq
f8ada32941f8c3ā€¦5647409e5affa0
1 in ā†’ 2 out7.5562 XPM225 B
ALTXQ3Pcā€¦VXY4hFHkAK7AR1xDā€¦PZS73NRf
67fc395fed11b0ā€¦2ac91657aa7fc9
1 in ā†’ 2 out7.0139 XPM226 B
ALc84ZB6ā€¦4Z1KmiXgAQn9yjxkā€¦t3Vrquof
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) ā€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

4.535 Ɨ 10ā¹ā“(95-digit number)
45353122686430828066ā€¦15565748104678209459
Discovered Prime Numbers
Lower: 2^k Ɨ origin āˆ’ 1 | Upper: 2^k Ɨ 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 ā€” Twin Prime Pair (origin Ā± 1)
origin āˆ’ 1
4.535 Ɨ 10ā¹ā“(95-digit number)
45353122686430828066ā€¦15565748104678209459
Verify on FactorDB ā†—Wolfram Alpha ā†—
origin + 1
4.535 Ɨ 10ā¹ā“(95-digit number)
45353122686430828066ā€¦15565748104678209461
Verify on FactorDB ā†—Wolfram Alpha ā†—
Difference: origin + 1 āˆ’ origin āˆ’ 1 = 2 (twin primes āœ“)
Level 1 ā€” Twin Prime Pair (2^1 Ɨ origin Ā± 1)
2^1 Ɨ origin āˆ’ 1
9.070 Ɨ 10ā¹ā“(95-digit number)
90706245372861656132ā€¦31131496209356418919
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^1 Ɨ origin + 1
9.070 Ɨ 10ā¹ā“(95-digit number)
90706245372861656132ā€¦31131496209356418921
Verify on FactorDB ā†—Wolfram Alpha ā†—
Difference: 2^1 Ɨ origin + 1 āˆ’ 2^1 Ɨ origin āˆ’ 1 = 2 (twin primes āœ“)
Level 2 ā€” Twin Prime Pair (2^2 Ɨ origin Ā± 1)
2^2 Ɨ origin āˆ’ 1
1.814 Ɨ 10ā¹āµ(96-digit number)
18141249074572331226ā€¦62262992418712837839
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^2 Ɨ origin + 1
1.814 Ɨ 10ā¹āµ(96-digit number)
18141249074572331226ā€¦62262992418712837841
Verify on FactorDB ā†—Wolfram Alpha ā†—
Difference: 2^2 Ɨ origin + 1 āˆ’ 2^2 Ɨ origin āˆ’ 1 = 2 (twin primes āœ“)
Level 3 ā€” Twin Prime Pair (2^3 Ɨ origin Ā± 1)
2^3 Ɨ origin āˆ’ 1
3.628 Ɨ 10ā¹āµ(96-digit number)
36282498149144662452ā€¦24525984837425675679
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^3 Ɨ origin + 1
3.628 Ɨ 10ā¹āµ(96-digit number)
36282498149144662452ā€¦24525984837425675681
Verify on FactorDB ā†—Wolfram Alpha ā†—
Difference: 2^3 Ɨ origin + 1 āˆ’ 2^3 Ɨ origin āˆ’ 1 = 2 (twin primes āœ“)
Level 4 ā€” Twin Prime Pair (2^4 Ɨ origin Ā± 1)
2^4 Ɨ origin āˆ’ 1
7.256 Ɨ 10ā¹āµ(96-digit number)
72564996298289324905ā€¦49051969674851351359
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^4 Ɨ origin + 1
7.256 Ɨ 10ā¹āµ(96-digit number)
72564996298289324905ā€¦49051969674851351361
Verify on FactorDB ā†—Wolfram Alpha ā†—
Difference: 2^4 Ɨ origin + 1 āˆ’ 2^4 Ɨ origin āˆ’ 1 = 2 (twin primes āœ“)

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 ā€” the large number shown above ā€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

ā˜…ā˜…ā˜†ā˜†ā˜†
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 Ɨ 3 Ɨ 5 Ɨ 7 Ɨ ā€¦), the result is the first prime in the chain. The origin is deliberately divisible by this primorial ā€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Ɨ Primorial (2Ā·3Ā·5Ā·7Ā·11Ā·ā€¦)
Source: Primecoin prime.cpp ā€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors ā€” 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 āˆ’ 1 and p+2 = origin/primorial + 1
Cross-reference on Chainz Explorer
Circulating Supply:57,614,307 XPMĀ·at block #6,796,287 Ā· updates every 60s
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