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Block #2,792,575

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/13/2018, 7:33:37 PM Β· Difficulty 11.6761 Β· 4,049,931 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
7942a845daa055a83db28b9e4ac29e0676252356b9dfd9e2115e882e33212210
View on Chainz β†—

Height

#2,792,575

Difficulty

11.676100

Transactions

1

Size

201 B

Version

2

Bits

0bad14e2

Nonce

611,323,940

Timestamp

8/13/2018, 7:33:37 PM

Confirmations

4,049,931

Mined by

⛏️ P2SHAZeUBR5cfpRRJaeqPX9dfeS8W3wNuyWd6N

Merkle Root

a575d149399a577fa124305ff51b283096d6b665a989c9df075c2d4fb29d5d52
Transactions (1)
Coinbasea575d149399a57…5c2d4fb29d5d52
1 in β†’ 1 out7.3200 XPM110 B
AZeUBR5c…wNuyWd6N
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.

8.427 Γ— 10⁹⁡(96-digit number)
84277029696577068588…55073046360494814719
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
8.427 Γ— 10⁹⁡(96-digit number)
84277029696577068588…55073046360494814719
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.427 Γ— 10⁹⁡(96-digit number)
84277029696577068588…55073046360494814721
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
1.685 Γ— 10⁹⁢(97-digit number)
16855405939315413717…10146092720989629439
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.685 Γ— 10⁹⁢(97-digit number)
16855405939315413717…10146092720989629441
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
3.371 Γ— 10⁹⁢(97-digit number)
33710811878630827435…20292185441979258879
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.371 Γ— 10⁹⁢(97-digit number)
33710811878630827435…20292185441979258881
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
6.742 Γ— 10⁹⁢(97-digit number)
67421623757261654871…40584370883958517759
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.742 Γ— 10⁹⁢(97-digit number)
67421623757261654871…40584370883958517761
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
1.348 Γ— 10⁹⁷(98-digit number)
13484324751452330974…81168741767917035519
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.348 Γ— 10⁹⁷(98-digit number)
13484324751452330974…81168741767917035521
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
2.696 Γ— 10⁹⁷(98-digit number)
26968649502904661948…62337483535834071039
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:57,984,466 XPMΒ·at block #6,842,505 Β· updates every 60s
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