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Block #2,634,885

TWNLength 11ā˜…ā˜…ā˜…ā˜†ā˜†

Bi-Twin Chain Ā· Discovered 4/29/2018, 1:30:41 AM Ā· Difficulty 11.2769 Ā· 4,205,350 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
3a9987f10b77d37e9b70a08d9651b84849615c4e4c4c2a6663fb161379b920bb
View on Chainz ā†—

Height

#2,634,885

Difficulty

11.276868

Transactions

5

Size

1.37 KB

Version

2

Bits

0b46e0da

Nonce

21,879,247

Timestamp

4/29/2018, 1:30:41 AM

Confirmations

4,205,350

Mined by

ā›ļø P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

790ff5b4fe074dfbb647792fd6dc8a2e90ad840632c5e8e506bd1bca16d55f67
Transactions (5)
Coinbase5fe6de2922c417ā€¦77367582821b8f
1 in ā†’ 1 out7.8900 XPM110 B
Adqah8zhā€¦1WwoHJ9t
713933111fb5caā€¦8084d35e1fee67
1 in ā†’ 2 out232353.0544 XPM227 B
Ad1nzX5aā€¦3wgBTFzdAKyMpAerā€¦j5hyAD7o
ac1650990858a8ā€¦586f8d5b8c9f01
3 in ā†’ 2 out20.5900 XPM521 B
ARsiPW1rā€¦oR9DimrEAPdvRHFQā€¦9QAq1Mof
79c55c07c76909ā€¦dabeb7aba4b333
1 in ā†’ 2 out230734.1794 XPM226 B
APCX6jdiā€¦MToeULJFAZJCoFNrā€¦kYH1xiss
da963d72248574ā€¦3e52a8eb36e7d3
1 in ā†’ 2 out230540.0648 XPM227 B
AGez8MDnā€¦5LaaQTrqAcJv73szā€¦N8w8Kfts
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.

1.910 Ɨ 10ā¹ā“(95-digit number)
19108335153098882150ā€¦21000222371486598959
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
1.910 Ɨ 10ā¹ā“(95-digit number)
19108335153098882150ā€¦21000222371486598959
Verify on FactorDB ā†—Wolfram Alpha ā†—
origin + 1
1.910 Ɨ 10ā¹ā“(95-digit number)
19108335153098882150ā€¦21000222371486598961
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
3.821 Ɨ 10ā¹ā“(95-digit number)
38216670306197764301ā€¦42000444742973197919
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^1 Ɨ origin + 1
3.821 Ɨ 10ā¹ā“(95-digit number)
38216670306197764301ā€¦42000444742973197921
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
7.643 Ɨ 10ā¹ā“(95-digit number)
76433340612395528602ā€¦84000889485946395839
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^2 Ɨ origin + 1
7.643 Ɨ 10ā¹ā“(95-digit number)
76433340612395528602ā€¦84000889485946395841
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
1.528 Ɨ 10ā¹āµ(96-digit number)
15286668122479105720ā€¦68001778971892791679
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^3 Ɨ origin + 1
1.528 Ɨ 10ā¹āµ(96-digit number)
15286668122479105720ā€¦68001778971892791681
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
3.057 Ɨ 10ā¹āµ(96-digit number)
30573336244958211440ā€¦36003557943785583359
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^4 Ɨ origin + 1
3.057 Ɨ 10ā¹āµ(96-digit number)
30573336244958211440ā€¦36003557943785583361
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
6.114 Ɨ 10ā¹āµ(96-digit number)
61146672489916422881ā€¦72007115887571166719
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:57,966,191 XPMĀ·at block #6,840,234 Ā· updates every 60s
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