XPM Prime Explorer symbol
XPMPrime Explorer

Block #1,245,256

TWNLength 10ā˜…ā˜…ā˜†ā˜†ā˜†

Bi-Twin Chain Ā· Discovered 9/20/2015, 8:04:10 PM Ā· Difficulty 10.7443 Ā· 5,571,231 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
fa72ff3dcc7ee3a0c7b8cb6e8c43225150144c30e765c9cee94eef5bec2b2229
View on Chainz ā†—

Height

#1,245,256

Difficulty

10.744307

Transactions

2

Size

1004 B

Version

2

Bits

0abe8aea

Nonce

21,867,907

Timestamp

9/20/2015, 8:04:10 PM

Confirmations

5,571,231

Mined by

ā›ļø P2SHAGQpbecZD6Saq2XF8gkKLvvMJ96YGcgHQw

Merkle Root

b7864cc3b09b6099bc798c453e3b71a2c680d949afdbd294c923302d7e7fb15c
Transactions (2)
Coinbasecaffae0ebc46c8ā€¦5a6de6d663220b
1 in ā†’ 1 out8.6600 XPM110 B
AGQpbecZā€¦6YGcgHQw
102993b0782f45ā€¦9ef37d90d56c2b
1 in ā†’ 19 out174.9077 XPM804 B
ALQG96NKā€¦5zPi39NBARewGJdcā€¦LqaD2w1CAeAgDyTnā€¦8uKNgvMRAcwhnbjkā€¦oBcdJLtwAcRQ166Hā€¦ZxPA7evd
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.

4.867 Ɨ 10ā¹ā“(95-digit number)
48678930085492641632ā€¦16302869138179476479
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
4.867 Ɨ 10ā¹ā“(95-digit number)
48678930085492641632ā€¦16302869138179476479
Verify on FactorDB ā†—Wolfram Alpha ā†—
origin + 1
4.867 Ɨ 10ā¹ā“(95-digit number)
48678930085492641632ā€¦16302869138179476481
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
9.735 Ɨ 10ā¹ā“(95-digit number)
97357860170985283265ā€¦32605738276358952959
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^1 Ɨ origin + 1
9.735 Ɨ 10ā¹ā“(95-digit number)
97357860170985283265ā€¦32605738276358952961
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
1.947 Ɨ 10ā¹āµ(96-digit number)
19471572034197056653ā€¦65211476552717905919
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^2 Ɨ origin + 1
1.947 Ɨ 10ā¹āµ(96-digit number)
19471572034197056653ā€¦65211476552717905921
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
3.894 Ɨ 10ā¹āµ(96-digit number)
38943144068394113306ā€¦30422953105435811839
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^3 Ɨ origin + 1
3.894 Ɨ 10ā¹āµ(96-digit number)
38943144068394113306ā€¦30422953105435811841
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
7.788 Ɨ 10ā¹āµ(96-digit number)
77886288136788226612ā€¦60845906210871623679
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^4 Ɨ origin + 1
7.788 Ɨ 10ā¹āµ(96-digit number)
77886288136788226612ā€¦60845906210871623681
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:57,776,023 XPMĀ·at block #6,816,486 Ā· updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.
Privacy PolicyĀ·
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

Cookie Preferences

We use cookies to enhance your experience. Some are essential for the site to function, while others help us understand how you use the site.

Ā·Privacy Policy