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Block #3,157,903

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 4/27/2019, 3:13:01 PM Β· Difficulty 11.3233 Β· 3,687,119 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
0932fc1af653653ad93863c52877a6f3340449628e32b28787634b39d33a90b0
View on Chainz β†—

Height

#3,157,903

Difficulty

11.323252

Transactions

2

Size

3.13 KB

Version

2

Bits

0b52c0a5

Nonce

371,562,836

Timestamp

4/27/2019, 3:13:01 PM

Confirmations

3,687,119

Mined by

⛏️ 0AbXwmGxDc5ZxwPwgT1QckjRUmF4XXYP765

Merkle Root

5f4a4641a7b40898cfad1fafde9e22ffeb52707b473c1c4ffff662340b7fe8ca
Transactions (2)
Coinbase9eabfdf7546bba…ec9bcdc516b306
1 in β†’ 1 out7.8700 XPM110 B
AbXwmGxD…4XXYP765
aa742e68c1f908…306e63943d12ad
20 in β†’ 1 out3190.4651 XPM2.93 KB
AQpirNZH…YMX3K11g
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.

4.092 Γ— 10⁹⁢(97-digit number)
40925392226569556139…43218989371554529279
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
4.092 Γ— 10⁹⁢(97-digit number)
40925392226569556139…43218989371554529279
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.092 Γ— 10⁹⁢(97-digit number)
40925392226569556139…43218989371554529281
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
8.185 Γ— 10⁹⁢(97-digit number)
81850784453139112279…86437978743109058559
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.185 Γ— 10⁹⁢(97-digit number)
81850784453139112279…86437978743109058561
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
1.637 Γ— 10⁹⁷(98-digit number)
16370156890627822455…72875957486218117119
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.637 Γ— 10⁹⁷(98-digit number)
16370156890627822455…72875957486218117121
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
3.274 Γ— 10⁹⁷(98-digit number)
32740313781255644911…45751914972436234239
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.274 Γ— 10⁹⁷(98-digit number)
32740313781255644911…45751914972436234241
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
6.548 Γ— 10⁹⁷(98-digit number)
65480627562511289823…91503829944872468479
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.548 Γ— 10⁹⁷(98-digit number)
65480627562511289823…91503829944872468481
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
1.309 Γ— 10⁹⁸(99-digit number)
13096125512502257964…83007659889744936959
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:58,004,600 XPMΒ·at block #6,845,021 Β· updates every 60s
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