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Block #2,244,099

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/9/2017, 4:23:17 PM Β· Difficulty 10.9470 Β· 4,592,823 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
7e0287089df6b54cf641712e5182d09c27be1e74fe9784b609f8dcf968c8d64c
View on Chainz β†—

Height

#2,244,099

Difficulty

10.947014

Transactions

2

Size

12.40 KB

Version

2

Bits

0af26f7d

Nonce

256,271,638

Timestamp

8/9/2017, 4:23:17 PM

Confirmations

4,592,823

Mined by

⛏️ P2SHAXTPRuiJeT3wLeA9KK4YxvnDN9258swhcH

Merkle Root

850db5d696c1970a5cde6e6bdc169c91b883cb03da734e7632cfd8874f1f836c
Transactions (2)
Coinbase6c1366cc4e4f1e…221dd5e6bd3d7c
1 in β†’ 1 out8.4800 XPM110 B
AXTPRuiJ…258swhcH
a6f0738af9d6f7…6a905dbb973a2f
84 in β†’ 2 out946.8778 XPM12.20 KB
AefEMpwP…gBcK6XwiAaJdN68U…29ZgLz2p
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.

3.036 Γ— 10⁹⁷(98-digit number)
30369863217133634826…85208502790854717439
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
3.036 Γ— 10⁹⁷(98-digit number)
30369863217133634826…85208502790854717439
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.036 Γ— 10⁹⁷(98-digit number)
30369863217133634826…85208502790854717441
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
6.073 Γ— 10⁹⁷(98-digit number)
60739726434267269652…70417005581709434879
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.073 Γ— 10⁹⁷(98-digit number)
60739726434267269652…70417005581709434881
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
1.214 Γ— 10⁹⁸(99-digit number)
12147945286853453930…40834011163418869759
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.214 Γ— 10⁹⁸(99-digit number)
12147945286853453930…40834011163418869761
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
2.429 Γ— 10⁹⁸(99-digit number)
24295890573706907861…81668022326837739519
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.429 Γ— 10⁹⁸(99-digit number)
24295890573706907861…81668022326837739521
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
4.859 Γ— 10⁹⁸(99-digit number)
48591781147413815722…63336044653675479039
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.859 Γ— 10⁹⁸(99-digit number)
48591781147413815722…63336044653675479041
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
9.718 Γ— 10⁹⁸(99-digit number)
97183562294827631444…26672089307350958079
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:57,939,671 XPMΒ·at block #6,836,921 Β· updates every 60s
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