XPM Prime Explorer symbol
XPMPrime Explorer

Block #2,121,355

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 5/17/2017, 11:33:39 PM Β· Difficulty 10.9131 Β· 4,705,956 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
0ca6b73e1bcfaae4626497e3a98437e5652b7b13b842e6a254e4af81c62084c5
View on Chainz β†—

Height

#2,121,355

Difficulty

10.913061

Transactions

2

Size

1.39 KB

Version

2

Bits

0ae9be5e

Nonce

158,008,519

Timestamp

5/17/2017, 11:33:39 PM

Confirmations

4,705,956

Mined by

⛏️ P2SHAe4kqkW5aoGt9oEkjAVrkpSWArzX4uoW5J

Merkle Root

21b56bda67fcf4ce7a42682552cdea46dc3c9a4704134a77eb380e8ff50c5390
Transactions (2)
Coinbase014afb129e4c33…c6531519eccf38
1 in β†’ 1 out8.4000 XPM110 B
Ae4kqkW5…zX4uoW5J
634b9e931184b7…7ea33f7e541554
8 in β†’ 1 out1199.9900 XPM1.20 KB
AH9oL2o5…rtGRkpc4
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.

4.195 Γ— 10⁹³(94-digit number)
41952272188427112831…33840601122654476799
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
4.195 Γ— 10⁹³(94-digit number)
41952272188427112831…33840601122654476799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.195 Γ— 10⁹³(94-digit number)
41952272188427112831…33840601122654476801
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
8.390 Γ— 10⁹³(94-digit number)
83904544376854225662…67681202245308953599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.390 Γ— 10⁹³(94-digit number)
83904544376854225662…67681202245308953601
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
1.678 Γ— 10⁹⁴(95-digit number)
16780908875370845132…35362404490617907199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.678 Γ— 10⁹⁴(95-digit number)
16780908875370845132…35362404490617907201
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
3.356 Γ— 10⁹⁴(95-digit number)
33561817750741690265…70724808981235814399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.356 Γ— 10⁹⁴(95-digit number)
33561817750741690265…70724808981235814401
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
6.712 Γ— 10⁹⁴(95-digit number)
67123635501483380530…41449617962471628799
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.712 Γ— 10⁹⁴(95-digit number)
67123635501483380530…41449617962471628801
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:57,862,600 XPMΒ·at block #6,827,310 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