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Block #2,018,843

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 3/11/2017, 8:05:43 PM Β· Difficulty 10.7161 Β· 4,825,987 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
fc4c3292501eb46546aa99a9b141320a243aba2a97508c4b19168dcacbbf7704
View on Chainz β†—

Height

#2,018,843

Difficulty

10.716114

Transactions

2

Size

57.94 KB

Version

2

Bits

0ab75338

Nonce

171,842,727

Timestamp

3/11/2017, 8:05:43 PM

Confirmations

4,825,987

Mined by

⛏️ P2SHAN9taQh43iqBzgUWuYi7t7Z3rAShYbvo9p

Merkle Root

b4ba913d05f432223cb8f95b539633c72eaa28f92748be373a79f36e1dbbbb17
Transactions (2)
Coinbase118fec891cee2e…e7c3c4f4618cce
1 in β†’ 1 out9.4200 XPM110 B
AN9taQh4…ShYbvo9p
7fd48945ab4a27…42f41e185e6186
399 in β†’ 2 out5381.0103 XPM57.75 KB
ARrjfR48…Tgspn3EuAGW8iVgz…xMg7SUHX
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.

2.631 Γ— 10⁹⁢(97-digit number)
26318109129844050389…00652675463944785919
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
2.631 Γ— 10⁹⁢(97-digit number)
26318109129844050389…00652675463944785919
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.631 Γ— 10⁹⁢(97-digit number)
26318109129844050389…00652675463944785921
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
5.263 Γ— 10⁹⁢(97-digit number)
52636218259688100778…01305350927889571839
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.263 Γ— 10⁹⁢(97-digit number)
52636218259688100778…01305350927889571841
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
1.052 Γ— 10⁹⁷(98-digit number)
10527243651937620155…02610701855779143679
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.052 Γ— 10⁹⁷(98-digit number)
10527243651937620155…02610701855779143681
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
2.105 Γ— 10⁹⁷(98-digit number)
21054487303875240311…05221403711558287359
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.105 Γ— 10⁹⁷(98-digit number)
21054487303875240311…05221403711558287361
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
4.210 Γ— 10⁹⁷(98-digit number)
42108974607750480622…10442807423116574719
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.210 Γ— 10⁹⁷(98-digit number)
42108974607750480622…10442807423116574721
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:58,003,049 XPMΒ·at block #6,844,829 Β· updates every 60s
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