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Block #2,736,084

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 7/6/2018, 5:32:00 AM Β· Difficulty 11.6083 Β· 4,106,862 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
ba8f3d88ea33d362c2df1f8bcc45225a68454f9c12f2f6af47e3324de8c7efb4
View on Chainz β†—

Height

#2,736,084

Difficulty

11.608273

Transactions

2

Size

871 B

Version

2

Bits

0b9bb7cb

Nonce

30,514,939

Timestamp

7/6/2018, 5:32:00 AM

Confirmations

4,106,862

Mined by

⛏️ P2SHAXH78btZezDutVS1t6uFNh4NqUwVk8zXMn

Merkle Root

962b759da15272fc45dfec2accfdb2e5d111f433cdea9eefcf9840c0f8915f5f
Transactions (2)
Coinbase27954bf96ca0c9…869752b2629407
1 in β†’ 1 out7.4200 XPM110 B
AXH78btZ…wVk8zXMn
5c96591f730605…962d52cafd3bec
4 in β†’ 2 out649.4851 XPM671 B
AVMKxXGS…7zFzUfPWAQmjqzoU…5U6sbve9
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.

1.082 Γ— 10⁹⁡(96-digit number)
10822570488372623983…03722462527501336479
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
1.082 Γ— 10⁹⁡(96-digit number)
10822570488372623983…03722462527501336479
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.082 Γ— 10⁹⁡(96-digit number)
10822570488372623983…03722462527501336481
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
2.164 Γ— 10⁹⁡(96-digit number)
21645140976745247966…07444925055002672959
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.164 Γ— 10⁹⁡(96-digit number)
21645140976745247966…07444925055002672961
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
4.329 Γ— 10⁹⁡(96-digit number)
43290281953490495933…14889850110005345919
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.329 Γ— 10⁹⁡(96-digit number)
43290281953490495933…14889850110005345921
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
8.658 Γ— 10⁹⁡(96-digit number)
86580563906980991866…29779700220010691839
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.658 Γ— 10⁹⁡(96-digit number)
86580563906980991866…29779700220010691841
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
1.731 Γ— 10⁹⁢(97-digit number)
17316112781396198373…59559400440021383679
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.731 Γ— 10⁹⁢(97-digit number)
17316112781396198373…59559400440021383681
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
3.463 Γ— 10⁹⁢(97-digit number)
34632225562792396746…19118800880042767359
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:57,987,919 XPMΒ·at block #6,842,945 Β· updates every 60s
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