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Block #2,613,483

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 4/14/2018, 12:28:50 PM Β· Difficulty 11.2069 Β· 4,219,851 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
a2360107504d6fe31c530ec8c77775b55b148ab6aae15ac4019a1bf33766ff42
View on Chainz β†—

Height

#2,613,483

Difficulty

11.206927

Transactions

2

Size

541 B

Version

2

Bits

0b34f92d

Nonce

998,435,315

Timestamp

4/14/2018, 12:28:50 PM

Confirmations

4,219,851

Mined by

⛏️ P2SHAPxzZYDcgeEcjPFx4XU6KBqYjQYEjxEPEV

Merkle Root

19100a42ff926ceeab6667bac9516dcd642d98f949b2d8092d3a5aa3a462ffdd
Transactions (2)
Coinbase1c02f3402ba5df…4faeb817196763
1 in β†’ 1 out7.9600 XPM110 B
APxzZYDc…YEjxEPEV
85f8da1cbe09f4…7712801ddbe5aa
2 in β†’ 1 out7.9900 XPM340 B
ASEhqc6y…uiLW8tms
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.

8.140 Γ— 10⁹⁢(97-digit number)
81402179671990311435…12605149442948231679
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
8.140 Γ— 10⁹⁢(97-digit number)
81402179671990311435…12605149442948231679
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.140 Γ— 10⁹⁢(97-digit number)
81402179671990311435…12605149442948231681
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
1.628 Γ— 10⁹⁷(98-digit number)
16280435934398062287…25210298885896463359
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.628 Γ— 10⁹⁷(98-digit number)
16280435934398062287…25210298885896463361
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
3.256 Γ— 10⁹⁷(98-digit number)
32560871868796124574…50420597771792926719
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.256 Γ— 10⁹⁷(98-digit number)
32560871868796124574…50420597771792926721
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
6.512 Γ— 10⁹⁷(98-digit number)
65121743737592249148…00841195543585853439
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.512 Γ— 10⁹⁷(98-digit number)
65121743737592249148…00841195543585853441
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
1.302 Γ— 10⁹⁸(99-digit number)
13024348747518449829…01682391087171706879
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.302 Γ— 10⁹⁸(99-digit number)
13024348747518449829…01682391087171706881
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
2.604 Γ— 10⁹⁸(99-digit number)
26048697495036899659…03364782174343413759
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:57,910,867 XPMΒ·at block #6,833,333 Β· updates every 60s
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