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Block #2,788,879

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/11/2018, 6:57:03 AM Β· Difficulty 11.6722 Β· 4,042,113 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
f7c808fa5f6e6a47cac5fd88a637a47b615fcbbb9515134c31d62d94278c2f42
View on Chainz β†—

Height

#2,788,879

Difficulty

11.672190

Transactions

2

Size

1.14 KB

Version

2

Bits

0bac14a4

Nonce

123,117,627

Timestamp

8/11/2018, 6:57:03 AM

Confirmations

4,042,113

Mined by

⛏️ P2SHAZtxQr2FMR4PURkVAAuK17mDJ17grUWrUz

Merkle Root

b3f0158c2c861dacf8798f391c7c277b163d8dc91082c74b40111ad09545c0e0
Transactions (2)
Coinbase15cc5789ff9887…44d7d9c1fd5506
1 in β†’ 1 out7.3400 XPM110 B
AZtxQr2F…7grUWrUz
2178b1a8d8318f…9cf201ce09fbf9
6 in β†’ 2 out220.1533 XPM967 B
AStTB15h…BiYNVMG6AY8PErqK…gv7kMfQz
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.

1.646 Γ— 10⁹⁢(97-digit number)
16461783595852996502…98441241350044838399
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
1.646 Γ— 10⁹⁢(97-digit number)
16461783595852996502…98441241350044838399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.646 Γ— 10⁹⁢(97-digit number)
16461783595852996502…98441241350044838401
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
3.292 Γ— 10⁹⁢(97-digit number)
32923567191705993005…96882482700089676799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.292 Γ— 10⁹⁢(97-digit number)
32923567191705993005…96882482700089676801
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
6.584 Γ— 10⁹⁢(97-digit number)
65847134383411986010…93764965400179353599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.584 Γ— 10⁹⁢(97-digit number)
65847134383411986010…93764965400179353601
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
1.316 Γ— 10⁹⁷(98-digit number)
13169426876682397202…87529930800358707199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.316 Γ— 10⁹⁷(98-digit number)
13169426876682397202…87529930800358707201
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
2.633 Γ— 10⁹⁷(98-digit number)
26338853753364794404…75059861600717414399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.633 Γ— 10⁹⁷(98-digit number)
26338853753364794404…75059861600717414401
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
5.267 Γ— 10⁹⁷(98-digit number)
52677707506729588808…50119723201434828799
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:57,892,076 XPMΒ·at block #6,830,991 Β· updates every 60s
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