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Block #3,441,051

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/20/2019, 12:39:52 PM Β· Difficulty 10.9786 Β· 3,385,794 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
e23fd66f332631a8fef40260542462ffbcc020539e36c585f05c5de4ec04b6c1
View on Chainz β†—

Height

#3,441,051

Difficulty

10.978613

Transactions

2

Size

539 B

Version

2

Bits

0afa865c

Nonce

1,293,668,383

Timestamp

11/20/2019, 12:39:52 PM

Confirmations

3,385,794

Mined by

⛏️ P2SHASiq2qtKTzQ7sbERFE8Jp8HjsgVMhmk7yL

Merkle Root

06601043b58ca85e7b8ac3f30ccf93891b6726f0923ce41b51bb432040a4e76d
Transactions (2)
Coinbaseac71567c207ecb…992e558af6dfce
1 in β†’ 1 out8.2900 XPM110 B
ASiq2qtK…VMhmk7yL
647d53ff29b439…33b0dab1467b45
2 in β†’ 2 out13.0900 XPM339 B
AeHXpz5Q…WLPHByEVAY51XUHW…FV3gaVcs
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.

1.697 Γ— 10⁹⁴(95-digit number)
16976050252369562328…96876176437569884159
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
1.697 Γ— 10⁹⁴(95-digit number)
16976050252369562328…96876176437569884159
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.697 Γ— 10⁹⁴(95-digit number)
16976050252369562328…96876176437569884161
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
3.395 Γ— 10⁹⁴(95-digit number)
33952100504739124656…93752352875139768319
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.395 Γ— 10⁹⁴(95-digit number)
33952100504739124656…93752352875139768321
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
6.790 Γ— 10⁹⁴(95-digit number)
67904201009478249312…87504705750279536639
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.790 Γ— 10⁹⁴(95-digit number)
67904201009478249312…87504705750279536641
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
1.358 Γ— 10⁹⁡(96-digit number)
13580840201895649862…75009411500559073279
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.358 Γ— 10⁹⁡(96-digit number)
13580840201895649862…75009411500559073281
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
2.716 Γ— 10⁹⁡(96-digit number)
27161680403791299725…50018823001118146559
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.716 Γ— 10⁹⁡(96-digit number)
27161680403791299725…50018823001118146561
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:57,858,926 XPMΒ·at block #6,826,844 Β· updates every 60s
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