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Block #2,226,149

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/28/2017, 3:01:26 AM Β· Difficulty 10.9478 Β· 4,617,066 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
a29f7e1bd1ba98fd6a90b4111ec7177f1d30e1905f0fd3f088e8508f10586a66
View on Chainz β†—

Height

#2,226,149

Difficulty

10.947846

Transactions

2

Size

539 B

Version

2

Bits

0af2a607

Nonce

120,075,865

Timestamp

7/28/2017, 3:01:26 AM

Confirmations

4,617,066

Mined by

⛏️ P2SHAGuRcf5Dcrr8kAggzALN4RcXKTbdW28AEj

Merkle Root

9f3cff0189673502664e4d802a8b077db6aa6f0901035d2f0153f29bfb6baec2
Transactions (2)
Coinbase919658138d1444…843b23bb8ff806
1 in β†’ 1 out8.3400 XPM110 B
AGuRcf5D…bdW28AEj
886e1822c4b86f…0e3c4afa6f9c75
2 in β†’ 1 out1052.9900 XPM339 B
AcxhUhX6…N8N8w2tm
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.

2.938 Γ— 10⁹⁡(96-digit number)
29385909689417050797…21329178613576785919
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
2.938 Γ— 10⁹⁡(96-digit number)
29385909689417050797…21329178613576785919
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.938 Γ— 10⁹⁡(96-digit number)
29385909689417050797…21329178613576785921
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
5.877 Γ— 10⁹⁡(96-digit number)
58771819378834101595…42658357227153571839
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.877 Γ— 10⁹⁡(96-digit number)
58771819378834101595…42658357227153571841
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
1.175 Γ— 10⁹⁢(97-digit number)
11754363875766820319…85316714454307143679
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.175 Γ— 10⁹⁢(97-digit number)
11754363875766820319…85316714454307143681
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
2.350 Γ— 10⁹⁢(97-digit number)
23508727751533640638…70633428908614287359
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.350 Γ— 10⁹⁢(97-digit number)
23508727751533640638…70633428908614287361
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
4.701 Γ— 10⁹⁢(97-digit number)
47017455503067281276…41266857817228574719
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.701 Γ— 10⁹⁢(97-digit number)
47017455503067281276…41266857817228574721
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,990,093 XPMΒ·at block #6,843,214 Β· updates every 60s
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