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Block #3,049,166

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 2/12/2019, 2:24:52 AM Β· Difficulty 10.9961 Β· 3,790,208 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
35f829ef0674a44634f3184eb47b5f84e59f8743f52ad3dd306bf752c41fe93e
View on Chainz β†—

Height

#3,049,166

Difficulty

10.996089

Transactions

2

Size

574 B

Version

2

Bits

0afeffab

Nonce

19,920,903

Timestamp

2/12/2019, 2:24:52 AM

Confirmations

3,790,208

Mined by

⛏️ P2SHAbXwmGxDc5ZxwPwgT1QckjRUmF4XXYP765

Merkle Root

a6bdbf598df640d83652da08bd48ec074501721cee0ab44207d1e287b0c5d256
Transactions (2)
Coinbase9e5eec3acea016…cbae8ed12a171e
1 in β†’ 1 out8.2700 XPM109 B
AbXwmGxD…4XXYP765
b2da9fd9e9d376…900aa9bd41308c
2 in β†’ 2 out491.7774 XPM374 B
AdQvg6BL…pK2RReFSAeTHTL7A…vT1872bk
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.

1.219 Γ— 10⁹⁢(97-digit number)
12192951155888071821…75595023598739599359
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
1.219 Γ— 10⁹⁢(97-digit number)
12192951155888071821…75595023598739599359
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.219 Γ— 10⁹⁢(97-digit number)
12192951155888071821…75595023598739599361
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
2.438 Γ— 10⁹⁢(97-digit number)
24385902311776143642…51190047197479198719
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.438 Γ— 10⁹⁢(97-digit number)
24385902311776143642…51190047197479198721
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
4.877 Γ— 10⁹⁢(97-digit number)
48771804623552287284…02380094394958397439
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.877 Γ— 10⁹⁢(97-digit number)
48771804623552287284…02380094394958397441
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
9.754 Γ— 10⁹⁢(97-digit number)
97543609247104574569…04760188789916794879
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.754 Γ— 10⁹⁢(97-digit number)
97543609247104574569…04760188789916794881
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
1.950 Γ— 10⁹⁷(98-digit number)
19508721849420914913…09520377579833589759
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.950 Γ— 10⁹⁷(98-digit number)
19508721849420914913…09520377579833589761
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
3.901 Γ— 10⁹⁷(98-digit number)
39017443698841829827…19040755159667179519
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:57,959,274 XPMΒ·at block #6,839,373 Β· updates every 60s
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