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Block #2,621,063

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 4/19/2018, 4:07:39 PM Β· Difficulty 11.2321 Β· 4,203,683 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
182e3eb8ab4918c00aa1e3959bf032a820001d4ab1a53662934b85fc4050f68c
View on Chainz β†—

Height

#2,621,063

Difficulty

11.232099

Transactions

2

Size

93.36 KB

Version

2

Bits

0b3b6ad0

Nonce

311,392,990

Timestamp

4/19/2018, 4:07:39 PM

Confirmations

4,203,683

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

07aedcd1fec91ae4f2ca2bea942bdf729265e64e5adf526c1ce8236e8825c118
Transactions (2)
Coinbase54a4090603bcc1…928884ea5878ce
1 in β†’ 1 out8.8700 XPM109 B
Adqah8zh…1WwoHJ9t
cbddc2079eddaf…21b1884d6f86dd
644 in β†’ 2 out210.0100 XPM93.17 KB
AK9eW1wk…MMJcpcSmALPF8J52…Hjw4BMsG
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.

8.953 Γ— 10⁹⁡(96-digit number)
89535321877585711904…79613713722692211199
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
8.953 Γ— 10⁹⁡(96-digit number)
89535321877585711904…79613713722692211199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.953 Γ— 10⁹⁡(96-digit number)
89535321877585711904…79613713722692211201
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
1.790 Γ— 10⁹⁢(97-digit number)
17907064375517142380…59227427445384422399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.790 Γ— 10⁹⁢(97-digit number)
17907064375517142380…59227427445384422401
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
3.581 Γ— 10⁹⁢(97-digit number)
35814128751034284761…18454854890768844799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.581 Γ— 10⁹⁢(97-digit number)
35814128751034284761…18454854890768844801
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
7.162 Γ— 10⁹⁢(97-digit number)
71628257502068569523…36909709781537689599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.162 Γ— 10⁹⁢(97-digit number)
71628257502068569523…36909709781537689601
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
1.432 Γ— 10⁹⁷(98-digit number)
14325651500413713904…73819419563075379199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.432 Γ— 10⁹⁷(98-digit number)
14325651500413713904…73819419563075379201
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
2.865 Γ— 10⁹⁷(98-digit number)
28651303000827427809…47638839126150758399
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:57,842,039 XPMΒ·at block #6,824,745 Β· updates every 60s
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