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Block #178,012

TWNLength 10ā˜…ā˜…ā˜†ā˜†ā˜†

Bi-Twin Chain Ā· Discovered 9/24/2013, 2:34:44 AM Ā· Difficulty 9.8632 Ā· 6,649,273 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b4f84811e89ab6e2784b8ece53e0e3760998a6449da3ded9a40bbbc06ab28942
View on Chainz ā†—

Height

#178,012

Difficulty

9.863189

Transactions

3

Size

2.19 KB

Version

2

Bits

09dcf9f9

Nonce

1,178,674

Timestamp

9/24/2013, 2:34:44 AM

Confirmations

6,649,273

Mined by

ā›ļø P2SHAGHfPnfwvbkrSRun1yEo92NJSRhTc5o83a

Merkle Root

a889e034933325fa4e9a1e650f80019c92a33b2838e650865083dc38bdd63a80
Transactions (3)
Coinbasec4bb3538be9e34ā€¦ca9766e463a7f8
1 in ā†’ 1 out10.2900 XPM109 B
AGHfPnfwā€¦hTc5o83a
431094582d206fā€¦fc40bc463a0842
15 in ā†’ 2 out144.6400 XPM1.78 KB
AMEQTzhgā€¦uNU6BQPjAUo3CdAYā€¦CxJp8W2N
982b4d26b286dfā€¦7bdae87cedce2c
1 in ā†’ 2 out5.1919 XPM226 B
ASeAvTZBā€¦Q7BaVSmSAP4exjFFā€¦2JJqgYei
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.

5.884 Ɨ 10ā¹ā“(95-digit number)
58841578949233667931ā€¦02548031688978999999
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
5.884 Ɨ 10ā¹ā“(95-digit number)
58841578949233667931ā€¦02548031688978999999
Verify on FactorDB ā†—Wolfram Alpha ā†—
origin + 1
5.884 Ɨ 10ā¹ā“(95-digit number)
58841578949233667931ā€¦02548031688979000001
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
1.176 Ɨ 10ā¹āµ(96-digit number)
11768315789846733586ā€¦05096063377957999999
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^1 Ɨ origin + 1
1.176 Ɨ 10ā¹āµ(96-digit number)
11768315789846733586ā€¦05096063377958000001
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
2.353 Ɨ 10ā¹āµ(96-digit number)
23536631579693467172ā€¦10192126755915999999
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^2 Ɨ origin + 1
2.353 Ɨ 10ā¹āµ(96-digit number)
23536631579693467172ā€¦10192126755916000001
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
4.707 Ɨ 10ā¹āµ(96-digit number)
47073263159386934345ā€¦20384253511831999999
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^3 Ɨ origin + 1
4.707 Ɨ 10ā¹āµ(96-digit number)
47073263159386934345ā€¦20384253511832000001
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
9.414 Ɨ 10ā¹āµ(96-digit number)
94146526318773868691ā€¦40768507023663999999
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^4 Ɨ origin + 1
9.414 Ɨ 10ā¹āµ(96-digit number)
94146526318773868691ā€¦40768507023664000001
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:57,862,388 XPMĀ·at block #6,827,284 Ā· updates every 60s
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