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Block #2,654,268

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/9/2018, 4:06:44 AM Β· Difficulty 11.7231 Β· 4,189,493 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
89deaf5f60cc99d26d37361fa22924da82aad12e16207cfb95b2e2c8d46460bb
View on Chainz β†—

Height

#2,654,268

Difficulty

11.723067

Transactions

1

Size

200 B

Version

2

Bits

0bb91ae9

Nonce

752,798,458

Timestamp

5/9/2018, 4:06:44 AM

Confirmations

4,189,493

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

38e343438c8d41a26f1f65f531d7510ff33ee1b217b4413e88b8edf13d5f196a
Transactions (1)
Coinbase38e343438c8d41…b8edf13d5f196a
1 in β†’ 1 out7.2600 XPM110 B
Adqah8zh…1WwoHJ9t
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.

4.066 Γ— 10⁹³(94-digit number)
40669325790928154066…24545948174566525879
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
4.066 Γ— 10⁹³(94-digit number)
40669325790928154066…24545948174566525879
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.066 Γ— 10⁹³(94-digit number)
40669325790928154066…24545948174566525881
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
8.133 Γ— 10⁹³(94-digit number)
81338651581856308133…49091896349133051759
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.133 Γ— 10⁹³(94-digit number)
81338651581856308133…49091896349133051761
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
1.626 Γ— 10⁹⁴(95-digit number)
16267730316371261626…98183792698266103519
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.626 Γ— 10⁹⁴(95-digit number)
16267730316371261626…98183792698266103521
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
3.253 Γ— 10⁹⁴(95-digit number)
32535460632742523253…96367585396532207039
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.253 Γ— 10⁹⁴(95-digit number)
32535460632742523253…96367585396532207041
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
6.507 Γ— 10⁹⁴(95-digit number)
65070921265485046507…92735170793064414079
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.507 Γ— 10⁹⁴(95-digit number)
65070921265485046507…92735170793064414081
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
1.301 Γ— 10⁹⁡(96-digit number)
13014184253097009301…85470341586128828159
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:57,994,461 XPMΒ·at block #6,843,760 Β· updates every 60s
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