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Block #2,918,092

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 11/11/2018, 3:05:48 AM Β· Difficulty 11.4094 Β· 3,924,118 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
e372e9ae4b753da5105bf4cdab0112005ad51fd827ab271cc1b6999e2b3cbfb6
View on Chainz β†—

Height

#2,918,092

Difficulty

11.409395

Transactions

1

Size

200 B

Version

2

Bits

0b68ce16

Nonce

19,935,110

Timestamp

11/11/2018, 3:05:48 AM

Confirmations

3,924,118

Mined by

⛏️ P2SHAZ3Tpn9nRLtHno9yngKGzZWp871EngArqQ

Merkle Root

b22bd228a36cec1807b26bb068d3b1407745cb9209de4fb2a3c0d901d87651de
Transactions (1)
Coinbaseb22bd228a36cec…c0d901d87651de
1 in β†’ 1 out7.6700 XPM109 B
AZ3Tpn9n…1EngArqQ
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.

1.535 Γ— 10⁹⁢(97-digit number)
15356527357937023139…09500760181471526399
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
1.535 Γ— 10⁹⁢(97-digit number)
15356527357937023139…09500760181471526399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.535 Γ— 10⁹⁢(97-digit number)
15356527357937023139…09500760181471526401
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
3.071 Γ— 10⁹⁢(97-digit number)
30713054715874046278…19001520362943052799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.071 Γ— 10⁹⁢(97-digit number)
30713054715874046278…19001520362943052801
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
6.142 Γ— 10⁹⁢(97-digit number)
61426109431748092556…38003040725886105599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.142 Γ— 10⁹⁢(97-digit number)
61426109431748092556…38003040725886105601
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
1.228 Γ— 10⁹⁷(98-digit number)
12285221886349618511…76006081451772211199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.228 Γ— 10⁹⁷(98-digit number)
12285221886349618511…76006081451772211201
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
2.457 Γ— 10⁹⁷(98-digit number)
24570443772699237022…52012162903544422399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.457 Γ— 10⁹⁷(98-digit number)
24570443772699237022…52012162903544422401
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
4.914 Γ— 10⁹⁷(98-digit number)
49140887545398474045…04024325807088844799
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,982,076 XPMΒ·at block #6,842,209 Β· updates every 60s
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