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Block #2,646,049

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/3/2018, 4:28:50 AM Β· Difficulty 11.7438 Β· 4,190,348 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
e630ac5cba82900bc5a3a65d80a90885a935e0b94b830fb0c1b5d702ababd48b
View on Chainz β†—

Height

#2,646,049

Difficulty

11.743811

Transactions

2

Size

577 B

Version

2

Bits

0bbe6a6b

Nonce

1,462,866,541

Timestamp

5/3/2018, 4:28:50 AM

Confirmations

4,190,348

Mined by

⛏️ P2SHALayVE1aHJG9hUVgk8hk1RHUWJ5Pr5aSuV

Merkle Root

e9d74da426dc6ceed98c753ab574ca61c891cb181e8b9c671791779a2d90ab89
Transactions (2)
Coinbaseadf7dbe1898991…f080eb8357a493
1 in β†’ 1 out7.2500 XPM110 B
ALayVE1a…5Pr5aSuV
b64b1fad80307b…ad091067bd8ea6
2 in β†’ 2 out3.3353 XPM375 B
AUMzbGAY…jZC41bzQAYpRCnQ3…X6HKvih6
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.

3.646 Γ— 10⁹⁸(99-digit number)
36463254572103768521…33551173375535022079
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
3.646 Γ— 10⁹⁸(99-digit number)
36463254572103768521…33551173375535022079
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.646 Γ— 10⁹⁸(99-digit number)
36463254572103768521…33551173375535022081
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
7.292 Γ— 10⁹⁸(99-digit number)
72926509144207537042…67102346751070044159
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.292 Γ— 10⁹⁸(99-digit number)
72926509144207537042…67102346751070044161
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
1.458 Γ— 10⁹⁹(100-digit number)
14585301828841507408…34204693502140088319
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.458 Γ— 10⁹⁹(100-digit number)
14585301828841507408…34204693502140088321
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
2.917 Γ— 10⁹⁹(100-digit number)
29170603657683014816…68409387004280176639
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.917 Γ— 10⁹⁹(100-digit number)
29170603657683014816…68409387004280176641
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
5.834 Γ— 10⁹⁹(100-digit number)
58341207315366029633…36818774008560353279
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.834 Γ— 10⁹⁹(100-digit number)
58341207315366029633…36818774008560353281
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
1.166 Γ— 10¹⁰⁰(101-digit number)
11668241463073205926…73637548017120706559
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:57,935,438 XPMΒ·at block #6,836,396 Β· updates every 60s
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