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XPMPrime Explorer

Block #2,679,148

TWNLength 11ā˜…ā˜…ā˜…ā˜†ā˜†

Bi-Twin Chain Ā· Discovered 5/26/2018, 7:41:45 PM Ā· Difficulty 11.6929 Ā· 4,157,774 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
5aa7925ef60385b654a75a8560c8a300a614213d383c0a16156a559ca67e63b3
View on Chainz ā†—

Height

#2,679,148

Difficulty

11.692906

Transactions

3

Size

1.65 KB

Version

2

Bits

0bb16250

Nonce

220,747,903

Timestamp

5/26/2018, 7:41:45 PM

Confirmations

4,157,774

Mined by

ā›ļø P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

5afd8adc04e0ccf521855fe183dcc6a7e96ac0765ecb64205bfd74a45912fb8c
Transactions (3)
Coinbase002e95749dac7dā€¦7bc43fa2b24dc8
1 in ā†’ 1 out7.3200 XPM110 B
Adqah8zhā€¦1WwoHJ9t
54fd7956a1eefbā€¦ea6c8c6307e5ba
4 in ā†’ 2 out3000.0105 XPM670 B
AJKzvN7vā€¦ngVEfttEAH3A2GJUā€¦NLYdkucb
47d80d3cacc5d2ā€¦2de9b7262fac72
5 in ā†’ 2 out1831.6412 XPM818 B
AJHHtshEā€¦jc4mKjCYAaZNTifAā€¦BqzEYTW6
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.

4.665 Ɨ 10ā¹ā“(95-digit number)
46654065508362487291ā€¦12395250419938665199
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
4.665 Ɨ 10ā¹ā“(95-digit number)
46654065508362487291ā€¦12395250419938665199
Verify on FactorDB ā†—Wolfram Alpha ā†—
origin + 1
4.665 Ɨ 10ā¹ā“(95-digit number)
46654065508362487291ā€¦12395250419938665201
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
9.330 Ɨ 10ā¹ā“(95-digit number)
93308131016724974583ā€¦24790500839877330399
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^1 Ɨ origin + 1
9.330 Ɨ 10ā¹ā“(95-digit number)
93308131016724974583ā€¦24790500839877330401
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
1.866 Ɨ 10ā¹āµ(96-digit number)
18661626203344994916ā€¦49581001679754660799
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^2 Ɨ origin + 1
1.866 Ɨ 10ā¹āµ(96-digit number)
18661626203344994916ā€¦49581001679754660801
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
3.732 Ɨ 10ā¹āµ(96-digit number)
37323252406689989833ā€¦99162003359509321599
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^3 Ɨ origin + 1
3.732 Ɨ 10ā¹āµ(96-digit number)
37323252406689989833ā€¦99162003359509321601
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
7.464 Ɨ 10ā¹āµ(96-digit number)
74646504813379979666ā€¦98324006719018643199
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^4 Ɨ origin + 1
7.464 Ɨ 10ā¹āµ(96-digit number)
74646504813379979666ā€¦98324006719018643201
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
1.492 Ɨ 10ā¹ā¶(97-digit number)
14929300962675995933ā€¦96648013438037286399
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:57,939,671 XPMĀ·at block #6,836,921 Ā· updates every 60s
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