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Block #3,241,953

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 6/26/2019, 3:41:26 PM Β· Difficulty 11.0036 Β· 3,594,680 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
3b627e1daac9274620b9c5bd89819a4a2f05c0567e520be15aae771e0f684da5
View on Chainz β†—

Height

#3,241,953

Difficulty

11.003600

Transactions

2

Size

12.23 KB

Version

2

Bits

0b00ebf5

Nonce

871,750,272

Timestamp

6/26/2019, 3:41:26 PM

Confirmations

3,594,680

Mined by

⛏️ P2SHASiq2qtKTzQ7sbERFE8Jp8HjsgVMhmk7yL

Merkle Root

0619df96168d355a962e09a7266be9d6e25a46a6cb576316ca4b2b4fc9817bfb
Transactions (2)
Coinbasef4fd2ef5540577…9e711ba6e82664
1 in β†’ 1 out8.3800 XPM110 B
ASiq2qtK…VMhmk7yL
4e325d867d5bd2…dd1fc896c14746
83 in β†’ 1 out2750.3500 XPM12.03 KB
AP2ikm3r…2qJRNrn6
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.

2.734 Γ— 10⁹⁴(95-digit number)
27340715815373896702…82479375045867638599
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
2.734 Γ— 10⁹⁴(95-digit number)
27340715815373896702…82479375045867638599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.734 Γ— 10⁹⁴(95-digit number)
27340715815373896702…82479375045867638601
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
5.468 Γ— 10⁹⁴(95-digit number)
54681431630747793405…64958750091735277199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.468 Γ— 10⁹⁴(95-digit number)
54681431630747793405…64958750091735277201
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
1.093 Γ— 10⁹⁡(96-digit number)
10936286326149558681…29917500183470554399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.093 Γ— 10⁹⁡(96-digit number)
10936286326149558681…29917500183470554401
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
2.187 Γ— 10⁹⁡(96-digit number)
21872572652299117362…59835000366941108799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.187 Γ— 10⁹⁡(96-digit number)
21872572652299117362…59835000366941108801
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
4.374 Γ— 10⁹⁡(96-digit number)
43745145304598234724…19670000733882217599
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.374 Γ— 10⁹⁡(96-digit number)
43745145304598234724…19670000733882217601
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
8.749 Γ— 10⁹⁡(96-digit number)
87490290609196469448…39340001467764435199
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:57,937,336 XPMΒ·at block #6,836,632 Β· updates every 60s
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