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Block #3,506,035

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 1/9/2020, 1:24:46 AM Β· Difficulty 10.9303 Β· 3,336,041 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
8d78a56eef7e678495ad07103e7ec1855d6c5c8489d56610d8e03c82d1b08bf7
View on Chainz β†—

Height

#3,506,035

Difficulty

10.930269

Transactions

1

Size

201 B

Version

2

Bits

0aee2615

Nonce

1,285,024,339

Timestamp

1/9/2020, 1:24:46 AM

Confirmations

3,336,041

Mined by

⛏️ P2SHASiq2qtKTzQ7sbERFE8Jp8HjsgVMhmk7yL

Merkle Root

051e616a1464f06a173a4d008b1c853b1efff8ef14a7c13cd1d6eb960d5def9b
Transactions (1)
Coinbase051e616a1464f0…d6eb960d5def9b
1 in β†’ 1 out8.3600 XPM110 B
ASiq2qtK…VMhmk7yL
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.

8.880 Γ— 10⁹⁢(97-digit number)
88807303876908461812…61654895848303001599
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
8.880 Γ— 10⁹⁢(97-digit number)
88807303876908461812…61654895848303001599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.880 Γ— 10⁹⁢(97-digit number)
88807303876908461812…61654895848303001601
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
1.776 Γ— 10⁹⁷(98-digit number)
17761460775381692362…23309791696606003199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.776 Γ— 10⁹⁷(98-digit number)
17761460775381692362…23309791696606003201
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
3.552 Γ— 10⁹⁷(98-digit number)
35522921550763384724…46619583393212006399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.552 Γ— 10⁹⁷(98-digit number)
35522921550763384724…46619583393212006401
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
7.104 Γ— 10⁹⁷(98-digit number)
71045843101526769449…93239166786424012799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.104 Γ— 10⁹⁷(98-digit number)
71045843101526769449…93239166786424012801
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
1.420 Γ— 10⁹⁸(99-digit number)
14209168620305353889…86478333572848025599
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.420 Γ— 10⁹⁸(99-digit number)
14209168620305353889…86478333572848025601
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
2.841 Γ— 10⁹⁸(99-digit number)
28418337240610707779…72956667145696051199
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:57,980,993 XPMΒ·at block #6,842,075 Β· updates every 60s
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