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Block #3,491,508

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/28/2019, 4:17:14 AM Β· Difficulty 10.9579 Β· 3,354,192 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
442ab5a773c401845c797418937849bc062828458fc96e1b746d706f4a19ec1b
View on Chainz β†—

Height

#3,491,508

Difficulty

10.957893

Transactions

1

Size

199 B

Version

2

Bits

0af5387d

Nonce

1,771,649,987

Timestamp

12/28/2019, 4:17:14 AM

Confirmations

3,354,192

Mined by

⛏️ xpmforall.orgAXfJqzUb1MbPSQVbWWFibnVbwWHXeXmjMzVisit pool β†—

Merkle Root

843f78f0c56bc3e1f9887d5b65784d0f732876e5670b47857a6d31962e3ff5a4
Transactions (1)
Coinbase843f78f0c56bc3…6d31962e3ff5a4
1 in β†’ 1 out8.3100 XPM109 B
AXfJqzUb…HXeXmjMz
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.

3.321 Γ— 10⁹⁡(96-digit number)
33213245724636245945…94339288208811950079
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
3.321 Γ— 10⁹⁡(96-digit number)
33213245724636245945…94339288208811950079
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.321 Γ— 10⁹⁡(96-digit number)
33213245724636245945…94339288208811950081
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
6.642 Γ— 10⁹⁡(96-digit number)
66426491449272491891…88678576417623900159
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.642 Γ— 10⁹⁡(96-digit number)
66426491449272491891…88678576417623900161
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
1.328 Γ— 10⁹⁢(97-digit number)
13285298289854498378…77357152835247800319
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.328 Γ— 10⁹⁢(97-digit number)
13285298289854498378…77357152835247800321
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
2.657 Γ— 10⁹⁢(97-digit number)
26570596579708996756…54714305670495600639
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.657 Γ— 10⁹⁢(97-digit number)
26570596579708996756…54714305670495600641
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
5.314 Γ— 10⁹⁢(97-digit number)
53141193159417993513…09428611340991201279
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.314 Γ— 10⁹⁢(97-digit number)
53141193159417993513…09428611340991201281
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:58,010,057 XPMΒ·at block #6,845,699 Β· updates every 60s
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