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Block #3,241,271

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 6/26/2019, 4:21:09 AM Β· Difficulty 11.0039 Β· 3,602,523 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
974a765ee7bc38ff8135c874dd5dd000751d68c41cedb4834910bb7638af78ac
View on Chainz β†—

Height

#3,241,271

Difficulty

11.003918

Transactions

2

Size

393 B

Version

2

Bits

0b0100bd

Nonce

861,800,132

Timestamp

6/26/2019, 4:21:09 AM

Confirmations

3,602,523

Mined by

⛏️ P2SHARbm48qRsZyALB7gqdgsMMKGGA9xQc8DBX

Merkle Root

a5813f83a57223793802cd292b4d05b7e88cdd50b9149ab7d310cc26e8e97a53
Transactions (2)
Coinbase0c748f23aaf70e…0970da2859a653
1 in β†’ 1 out8.2600 XPM110 B
ARbm48qR…9xQc8DBX
eff363fe408043…84575e00fd0c38
1 in β†’ 1 out140.1132 XPM192 B
AXXGfizT…aeWx1Cui
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.

7.402 Γ— 10⁹⁢(97-digit number)
74023270759814602023…43643139084364743039
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
7.402 Γ— 10⁹⁢(97-digit number)
74023270759814602023…43643139084364743039
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.402 Γ— 10⁹⁢(97-digit number)
74023270759814602023…43643139084364743041
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
1.480 Γ— 10⁹⁷(98-digit number)
14804654151962920404…87286278168729486079
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.480 Γ— 10⁹⁷(98-digit number)
14804654151962920404…87286278168729486081
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
2.960 Γ— 10⁹⁷(98-digit number)
29609308303925840809…74572556337458972159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.960 Γ— 10⁹⁷(98-digit number)
29609308303925840809…74572556337458972161
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
5.921 Γ— 10⁹⁷(98-digit number)
59218616607851681618…49145112674917944319
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.921 Γ— 10⁹⁷(98-digit number)
59218616607851681618…49145112674917944321
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
1.184 Γ— 10⁹⁸(99-digit number)
11843723321570336323…98290225349835888639
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.184 Γ— 10⁹⁸(99-digit number)
11843723321570336323…98290225349835888641
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
2.368 Γ— 10⁹⁸(99-digit number)
23687446643140672647…96580450699671777279
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:57,994,729 XPMΒ·at block #6,843,793 Β· updates every 60s
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