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Block #3,434,695

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 11/15/2019, 10:25:36 PM Β· Difficulty 10.9795 Β· 3,404,683 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b58d065cc9c23f5504c354e1fe060cfdb12911108f21d5b04ef914fb44b1c6b5
View on Chainz β†—

Height

#3,434,695

Difficulty

10.979486

Transactions

2

Size

1.86 KB

Version

2

Bits

0afabf9f

Nonce

1,016,662,399

Timestamp

11/15/2019, 10:25:36 PM

Confirmations

3,404,683

Mined by

⛏️ P2SHASiq2qtKTzQ7sbERFE8Jp8HjsgVMhmk7yL

Merkle Root

c8a247255b3ec85a48c779fab44d3493e57bbc8f9b740d5dcbde581cef17aafd
Transactions (2)
Coinbase10d53177489228…6d7cc65f73e9f9
1 in β†’ 1 out8.5700 XPM110 B
ASiq2qtK…VMhmk7yL
b70cc41452bcc6…8e0891de848a2b
11 in β†’ 2 out49788.6582 XPM1.67 KB
ANa4b37S…LJ96sHMuAXas8mJB…RCqnRtuC
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.

1.752 Γ— 10⁹⁷(98-digit number)
17525299987035370737…87250256349831249919
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
1.752 Γ— 10⁹⁷(98-digit number)
17525299987035370737…87250256349831249919
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.752 Γ— 10⁹⁷(98-digit number)
17525299987035370737…87250256349831249921
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
3.505 Γ— 10⁹⁷(98-digit number)
35050599974070741474…74500512699662499839
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.505 Γ— 10⁹⁷(98-digit number)
35050599974070741474…74500512699662499841
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
7.010 Γ— 10⁹⁷(98-digit number)
70101199948141482949…49001025399324999679
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.010 Γ— 10⁹⁷(98-digit number)
70101199948141482949…49001025399324999681
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
1.402 Γ— 10⁹⁸(99-digit number)
14020239989628296589…98002050798649999359
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.402 Γ— 10⁹⁸(99-digit number)
14020239989628296589…98002050798649999361
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
2.804 Γ— 10⁹⁸(99-digit number)
28040479979256593179…96004101597299998719
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.804 Γ— 10⁹⁸(99-digit number)
28040479979256593179…96004101597299998721
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
5.608 Γ— 10⁹⁸(99-digit number)
56080959958513186359…92008203194599997439
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:57,959,307 XPMΒ·at block #6,839,377 Β· updates every 60s
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