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XPMPrime Explorer

Block #3,085,628

TWNLength 11ā˜…ā˜…ā˜…ā˜†ā˜†

Bi-Twin Chain Ā· Discovered 3/9/2019, 4:39:56 PM Ā· Difficulty 11.0290 Ā· 3,756,245 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
0c2df3ae6c2b21c27f64c66bdae96051a213519409d19c1a624c93969f818a50
View on Chainz ā†—

Height

#3,085,628

Difficulty

11.029001

Transactions

4

Size

3.32 KB

Version

2

Bits

0b076ca3

Nonce

1,336,758,703

Timestamp

3/9/2019, 4:39:56 PM

Confirmations

3,756,245

Mined by

ā›ļø P2SHAbXwmGxDc5ZxwPwgT1QckjRUmF4XXYP765

Merkle Root

1886408bb4306fa75e4974485e2d711c8808a62f07698dc624ab6beedf22c6e5
Transactions (4)
Coinbasecae45bf2dbb720ā€¦103cd6e03130f3
1 in ā†’ 1 out8.2600 XPM110 B
AbXwmGxDā€¦4XXYP765
2d08ddd2c508d1ā€¦cb407eb90d061c
17 in ā†’ 1 out3148.6459 XPM2.49 KB
AZQgL5ktā€¦6NE43uZs
c0391f501cc404ā€¦581136b469897a
2 in ā†’ 2 out16.4300 XPM307 B
AWgB1G1wā€¦cAHg7VxPAL28K79eā€¦Vj55mbBR
83d1035d92df38ā€¦cfd21d7b272b16
2 in ā†’ 2 out14.6400 XPM339 B
ASbWpaKtā€¦zbWPgm7gAPVKWthFā€¦PMMxwRoz
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.

1.222 Ɨ 10ā¹āµ(96-digit number)
12220016426132361776ā€¦40307660031567648259
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
1.222 Ɨ 10ā¹āµ(96-digit number)
12220016426132361776ā€¦40307660031567648259
Verify on FactorDB ā†—Wolfram Alpha ā†—
origin + 1
1.222 Ɨ 10ā¹āµ(96-digit number)
12220016426132361776ā€¦40307660031567648261
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
2.444 Ɨ 10ā¹āµ(96-digit number)
24440032852264723552ā€¦80615320063135296519
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^1 Ɨ origin + 1
2.444 Ɨ 10ā¹āµ(96-digit number)
24440032852264723552ā€¦80615320063135296521
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
4.888 Ɨ 10ā¹āµ(96-digit number)
48880065704529447105ā€¦61230640126270593039
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^2 Ɨ origin + 1
4.888 Ɨ 10ā¹āµ(96-digit number)
48880065704529447105ā€¦61230640126270593041
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
9.776 Ɨ 10ā¹āµ(96-digit number)
97760131409058894211ā€¦22461280252541186079
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^3 Ɨ origin + 1
9.776 Ɨ 10ā¹āµ(96-digit number)
97760131409058894211ā€¦22461280252541186081
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
1.955 Ɨ 10ā¹ā¶(97-digit number)
19552026281811778842ā€¦44922560505082372159
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^4 Ɨ origin + 1
1.955 Ɨ 10ā¹ā¶(97-digit number)
19552026281811778842ā€¦44922560505082372161
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
3.910 Ɨ 10ā¹ā¶(97-digit number)
39104052563623557684ā€¦89845121010164744319
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:57,979,359 XPMĀ·at block #6,841,872 Ā· updates every 60s
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