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Block #2,782,719

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/7/2018, 3:45:46 AM Β· Difficulty 11.6581 Β· 4,061,281 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
64d861c31aeb9e2c997dedac18f2ff644e77bdd4f293cec93ce350108fbadb53
View on Chainz β†—

Height

#2,782,719

Difficulty

11.658061

Transactions

1

Size

199 B

Version

2

Bits

0ba876b5

Nonce

273,694,734

Timestamp

8/7/2018, 3:45:46 AM

Confirmations

4,061,281

Mined by

⛏️ P2SHAao9YhScEpmRMfGHijwnmGbrzJwrrACnFR

Merkle Root

2a098db64f156e08ac040884ce9bfa85630c9d3e70ca2ef6efc09678945d094a
Transactions (1)
Coinbase2a098db64f156e…c09678945d094a
1 in β†’ 1 out7.3500 XPM110 B
Aao9YhSc…wrrACnFR
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.

8.741 Γ— 10⁹¹(92-digit number)
87419194495987392091…59027493915925084539
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
8.741 Γ— 10⁹¹(92-digit number)
87419194495987392091…59027493915925084539
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.741 Γ— 10⁹¹(92-digit number)
87419194495987392091…59027493915925084541
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
1.748 Γ— 10⁹²(93-digit number)
17483838899197478418…18054987831850169079
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.748 Γ— 10⁹²(93-digit number)
17483838899197478418…18054987831850169081
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
3.496 Γ— 10⁹²(93-digit number)
34967677798394956836…36109975663700338159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.496 Γ— 10⁹²(93-digit number)
34967677798394956836…36109975663700338161
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
6.993 Γ— 10⁹²(93-digit number)
69935355596789913673…72219951327400676319
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.993 Γ— 10⁹²(93-digit number)
69935355596789913673…72219951327400676321
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
1.398 Γ— 10⁹³(94-digit number)
13987071119357982734…44439902654801352639
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.398 Γ— 10⁹³(94-digit number)
13987071119357982734…44439902654801352641
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
2.797 Γ— 10⁹³(94-digit number)
27974142238715965469…88879805309602705279
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:57,996,382 XPMΒ·at block #6,843,999 Β· updates every 60s
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