XPM Prime Explorer symbol
XPMPrime Explorer

Block #1,885,151

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/8/2016, 10:14:13 PM Β· Difficulty 10.7154 Β· 4,945,894 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
54e012b7ba91d71f6b693ec01170eb0746fc472209c7e61789c821d5ad0b2dc4
View on Chainz β†—

Height

#1,885,151

Difficulty

10.715400

Transactions

1

Size

243 B

Version

2

Bits

0ab7247b

Nonce

248,539,390

Timestamp

12/8/2016, 10:14:13 PM

Confirmations

4,945,894

Mined by

⛏️ P2SHAMeY5ZrV7AqtjFwPLjnwr3BDd53veG96Ko

Merkle Root

de445f5ff852a3ad61aeb0e3257d1dcff5a901ce369333ab62f8336fb068fc07
Transactions (1)
Coinbasede445f5ff852a3…f8336fb068fc07
1 in β†’ 2 out8.7000 XPM152 B
AMeY5ZrV…3veG96KoALPu3s2c…EJXLjVFh
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

2.041 Γ— 10⁹⁢(97-digit number)
20412294986132721278…78712329715835401279
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 2^k Γ— 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 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
2.041 Γ— 10⁹⁢(97-digit number)
20412294986132721278…78712329715835401279
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.041 Γ— 10⁹⁢(97-digit number)
20412294986132721278…78712329715835401281
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
4.082 Γ— 10⁹⁢(97-digit number)
40824589972265442556…57424659431670802559
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.082 Γ— 10⁹⁢(97-digit number)
40824589972265442556…57424659431670802561
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
8.164 Γ— 10⁹⁢(97-digit number)
81649179944530885112…14849318863341605119
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.164 Γ— 10⁹⁢(97-digit number)
81649179944530885112…14849318863341605121
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
1.632 Γ— 10⁹⁷(98-digit number)
16329835988906177022…29698637726683210239
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.632 Γ— 10⁹⁷(98-digit number)
16329835988906177022…29698637726683210241
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
3.265 Γ— 10⁹⁷(98-digit number)
32659671977812354044…59397275453366420479
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.265 Γ— 10⁹⁷(98-digit number)
32659671977812354044…59397275453366420481
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

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 β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜…β˜†β˜†β˜†
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 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” 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 βˆ’ 1 and p+2 = origin/primorial + 1
Cross-reference on Chainz Explorer
Circulating Supply:57,892,498 XPMΒ·at block #6,831,044 Β· 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 PolicyΒ·
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.

Β·Privacy Policy