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Block #2,845,041

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/18/2018, 3:34:18 PM Β· Difficulty 11.7289 Β· 3,998,050 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
00fc17e6495bfbb66233bb50c18e6f50d7716fc02e5868241f18291b311ce3df
View on Chainz β†—

Height

#2,845,041

Difficulty

11.728876

Transactions

2

Size

1018 B

Version

2

Bits

0bba97a2

Nonce

1,924,415,896

Timestamp

9/18/2018, 3:34:18 PM

Confirmations

3,998,050

Mined by

⛏️ P2SHASHJd6csLAeZUtUcyYFTgvZ1xjhwexcWpa

Merkle Root

93b4d3e411938d9a5a88a4d8c01655e076d65c2d56cc2c4fad8f14946b3420b8
Transactions (2)
Coinbaseb42a6f8f86fdf1…0939c490aadb95
1 in β†’ 1 out7.2700 XPM110 B
ASHJd6cs…hwexcWpa
f8cf679d0d2499…203f1f5239eb4b
5 in β†’ 2 out2328.0099 XPM817 B
AMF31yLC…F83pEiaGAKBrnwny…os3V5ekz
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.

1.895 Γ— 10⁹⁷(98-digit number)
18954900572402246566…79527713476149534719
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
1.895 Γ— 10⁹⁷(98-digit number)
18954900572402246566…79527713476149534719
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.895 Γ— 10⁹⁷(98-digit number)
18954900572402246566…79527713476149534721
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
3.790 Γ— 10⁹⁷(98-digit number)
37909801144804493133…59055426952299069439
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.790 Γ— 10⁹⁷(98-digit number)
37909801144804493133…59055426952299069441
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
7.581 Γ— 10⁹⁷(98-digit number)
75819602289608986266…18110853904598138879
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.581 Γ— 10⁹⁷(98-digit number)
75819602289608986266…18110853904598138881
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
1.516 Γ— 10⁹⁸(99-digit number)
15163920457921797253…36221707809196277759
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.516 Γ— 10⁹⁸(99-digit number)
15163920457921797253…36221707809196277761
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
3.032 Γ— 10⁹⁸(99-digit number)
30327840915843594506…72443415618392555519
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.032 Γ— 10⁹⁸(99-digit number)
30327840915843594506…72443415618392555521
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
6.065 Γ— 10⁹⁸(99-digit number)
60655681831687189013…44886831236785111039
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:57,989,090 XPMΒ·at block #6,843,090 Β· updates every 60s
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