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Block #2,681,996

TWNLength 11ā˜…ā˜…ā˜…ā˜†ā˜†

Bi-Twin Chain Ā· Discovered 5/28/2018, 7:49:55 PM Ā· Difficulty 11.6906 Ā· 4,157,355 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
6b826eb335a69dd1a921b54d52b8929db9288cb325074c697b8b0e176dfd1b14
View on Chainz ā†—

Height

#2,681,996

Difficulty

11.690586

Transactions

4

Size

1.08 KB

Version

2

Bits

0bb0ca42

Nonce

562,811,651

Timestamp

5/28/2018, 7:49:55 PM

Confirmations

4,157,355

Mined by

ā›ļø P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

7068710bcd6e67267bcc4b190df464d02c6b6af2b193a985048b188d2be35bab
Transactions (4)
Coinbased9a65360b29247ā€¦3dd546d3a322a9
1 in ā†’ 1 out7.3300 XPM110 B
Adqah8zhā€¦1WwoHJ9t
95587ea29f6484ā€¦e1078533fe2f39
2 in ā†’ 2 out10.5354 XPM339 B
AbxbAUaLā€¦uX3gA9SKAQTfdhSVā€¦rdSgvZ7S
27f4411c4591c8ā€¦70d76ed5623365
2 in ā†’ 2 out11.5025 XPM342 B
AeuBwUG8ā€¦vabnX4S9AbNUu9xrā€¦SFUXCj5W
ea428403a029c2ā€¦8dd2a8b812e0b4
1 in ā†’ 2 out1.6544 XPM225 B
AZe1X6QXā€¦uXp9TafdAMFxoiZVā€¦2UX5WRMn
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.

5.723 Ɨ 10ā¹ā“(95-digit number)
57232872769110691232ā€¦41768101510672890959
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
5.723 Ɨ 10ā¹ā“(95-digit number)
57232872769110691232ā€¦41768101510672890959
Verify on FactorDB ā†—Wolfram Alpha ā†—
origin + 1
5.723 Ɨ 10ā¹ā“(95-digit number)
57232872769110691232ā€¦41768101510672890961
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
1.144 Ɨ 10ā¹āµ(96-digit number)
11446574553822138246ā€¦83536203021345781919
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^1 Ɨ origin + 1
1.144 Ɨ 10ā¹āµ(96-digit number)
11446574553822138246ā€¦83536203021345781921
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
2.289 Ɨ 10ā¹āµ(96-digit number)
22893149107644276493ā€¦67072406042691563839
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^2 Ɨ origin + 1
2.289 Ɨ 10ā¹āµ(96-digit number)
22893149107644276493ā€¦67072406042691563841
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
4.578 Ɨ 10ā¹āµ(96-digit number)
45786298215288552986ā€¦34144812085383127679
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^3 Ɨ origin + 1
4.578 Ɨ 10ā¹āµ(96-digit number)
45786298215288552986ā€¦34144812085383127681
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
9.157 Ɨ 10ā¹āµ(96-digit number)
91572596430577105972ā€¦68289624170766255359
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^4 Ɨ origin + 1
9.157 Ɨ 10ā¹āµ(96-digit number)
91572596430577105972ā€¦68289624170766255361
Verify on FactorDB ā†—Wolfram Alpha ā†—
Difference: 2^4 Ɨ origin + 1 āˆ’ 2^4 Ɨ origin āˆ’ 1 = 2 (twin primes āœ“)
Level 5 ā€” Twin Prime Pair (2^5 Ɨ origin Ā± 1)
2^5 Ɨ origin āˆ’ 1
1.831 Ɨ 10ā¹ā¶(97-digit number)
18314519286115421194ā€¦36579248341532510719
Verify on FactorDB ā†—Wolfram Alpha ā†—

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 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
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 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:57,959,094 XPMĀ·at block #6,839,350 Ā· updates every 60s
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