XPM Prime Explorer symbol
XPMPrime Explorer

Block #1,570,547

TWNLength 10ā˜…ā˜…ā˜†ā˜†ā˜†

Bi-Twin Chain Ā· Discovered 5/3/2016, 9:06:01 PM Ā· Difficulty 10.7479 Ā· 5,256,028 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
65b0746a43aba1099c83ccaf3bdce89aae1bfb1024b16f24e2098b60cae90c53
View on Chainz ā†—

Height

#1,570,547

Difficulty

10.747914

Transactions

2

Size

1003 B

Version

2

Bits

0abf7751

Nonce

57,824,089

Timestamp

5/3/2016, 9:06:01 PM

Confirmations

5,256,028

Mined by

ā›ļø P2SHAT2UjFbUoKPfYSUbgkbHgwC23H66FwVdiN

Merkle Root

f2f71f3bfc1aa20918b16fb69f444e68d11877278a2b1736c26d5b70db311f4d
Transactions (2)
Coinbase7f4ca191b4621fā€¦b69c12ef33f569
1 in ā†’ 1 out8.6500 XPM109 B
AT2UjFbUā€¦66FwVdiN
0899f56241eea3ā€¦1343db72cc5355
1 in ā†’ 19 out142.5524 XPM804 B
AK7Ffemuā€¦T2CVJbxKAZ7bdUiQā€¦VWjibCPnAYqkP9H7ā€¦2Gp2G7WXASZkHcFrā€¦fYFhuutzAQ1gep9vā€¦JXXhqJ18
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.

1.043 Ɨ 10ā¹āµ(96-digit number)
10433005903303887983ā€¦80991656168686880479
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
1.043 Ɨ 10ā¹āµ(96-digit number)
10433005903303887983ā€¦80991656168686880479
Verify on FactorDB ā†—Wolfram Alpha ā†—
origin + 1
1.043 Ɨ 10ā¹āµ(96-digit number)
10433005903303887983ā€¦80991656168686880481
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
2.086 Ɨ 10ā¹āµ(96-digit number)
20866011806607775967ā€¦61983312337373760959
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^1 Ɨ origin + 1
2.086 Ɨ 10ā¹āµ(96-digit number)
20866011806607775967ā€¦61983312337373760961
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
4.173 Ɨ 10ā¹āµ(96-digit number)
41732023613215551935ā€¦23966624674747521919
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^2 Ɨ origin + 1
4.173 Ɨ 10ā¹āµ(96-digit number)
41732023613215551935ā€¦23966624674747521921
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
8.346 Ɨ 10ā¹āµ(96-digit number)
83464047226431103871ā€¦47933249349495043839
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^3 Ɨ origin + 1
8.346 Ɨ 10ā¹āµ(96-digit number)
83464047226431103871ā€¦47933249349495043841
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
1.669 Ɨ 10ā¹ā¶(97-digit number)
16692809445286220774ā€¦95866498698990087679
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^4 Ɨ origin + 1
1.669 Ɨ 10ā¹ā¶(97-digit number)
16692809445286220774ā€¦95866498698990087681
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:57,856,749 XPMĀ·at block #6,826,574 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