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Block #2,795,613

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/15/2018, 9:14:21 PM Β· Difficulty 11.6799 Β· 4,048,287 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
4f59b86cd0f51fb4a992fc1383b7027a2d37842530e0411bccbc1b47a3ed0e2a
View on Chainz β†—

Height

#2,795,613

Difficulty

11.679919

Transactions

1

Size

201 B

Version

2

Bits

0bae0f28

Nonce

365,144,141

Timestamp

8/15/2018, 9:14:21 PM

Confirmations

4,048,287

Mined by

⛏️ P2SHAVWC4jBNgDRAJ5KExbkxfgkVPz3bw8P4A6

Merkle Root

644c1063a58487ceb7529bd5214285d560e5b88b88c7fbfbdd3dc7d3ce057ed9
Transactions (1)
Coinbase644c1063a58487…3dc7d3ce057ed9
1 in β†’ 1 out7.3200 XPM110 B
AVWC4jBN…3bw8P4A6
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.

5.138 Γ— 10⁹⁷(98-digit number)
51389289841514270254…60841427095483596799
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
5.138 Γ— 10⁹⁷(98-digit number)
51389289841514270254…60841427095483596799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.138 Γ— 10⁹⁷(98-digit number)
51389289841514270254…60841427095483596801
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
1.027 Γ— 10⁹⁸(99-digit number)
10277857968302854050…21682854190967193599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.027 Γ— 10⁹⁸(99-digit number)
10277857968302854050…21682854190967193601
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
2.055 Γ— 10⁹⁸(99-digit number)
20555715936605708101…43365708381934387199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.055 Γ— 10⁹⁸(99-digit number)
20555715936605708101…43365708381934387201
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
4.111 Γ— 10⁹⁸(99-digit number)
41111431873211416203…86731416763868774399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.111 Γ— 10⁹⁸(99-digit number)
41111431873211416203…86731416763868774401
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
8.222 Γ— 10⁹⁸(99-digit number)
82222863746422832407…73462833527737548799
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
8.222 Γ— 10⁹⁸(99-digit number)
82222863746422832407…73462833527737548801
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
1.644 Γ— 10⁹⁹(100-digit number)
16444572749284566481…46925667055475097599
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:57,995,571 XPMΒ·at block #6,843,899 Β· updates every 60s
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