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Block #1,518,884

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 3/30/2016, 3:19:58 PM Β· Difficulty 10.5946 Β· 5,306,657 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
f7c23981de692f9491c7b665816cd98dc752a51b30a39a3a4d9a5a4f0e1dc03a
View on Chainz β†—

Height

#1,518,884

Difficulty

10.594627

Transactions

2

Size

25.13 KB

Version

2

Bits

0a983977

Nonce

356,454,063

Timestamp

3/30/2016, 3:19:58 PM

Confirmations

5,306,657

Mined by

⛏️ P2SHAXjLxCHk5m1D6nGEUWxddhQG3aQaYivfnK

Merkle Root

9ea258c2a51c7ba1382524330c350f6a8ae7c5c17eade00a7d410ff34a58b9f3
Transactions (2)
Coinbaseb51546a766989b…6a4c7554c5d1ba
1 in β†’ 1 out9.2400 XPM109 B
AXjLxCHk…QaYivfnK
1dbc752afc5110…9ca31ac06b3ada
172 in β†’ 2 out100000.0100 XPM24.93 KB
AYKArr5V…V9VqiqCZAYEoV5uX…Hpcoodm1
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.

2.485 Γ— 10⁹⁴(95-digit number)
24852339190860676984…91745385944234135679
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
2.485 Γ— 10⁹⁴(95-digit number)
24852339190860676984…91745385944234135679
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.485 Γ— 10⁹⁴(95-digit number)
24852339190860676984…91745385944234135681
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
4.970 Γ— 10⁹⁴(95-digit number)
49704678381721353968…83490771888468271359
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.970 Γ— 10⁹⁴(95-digit number)
49704678381721353968…83490771888468271361
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
9.940 Γ— 10⁹⁴(95-digit number)
99409356763442707937…66981543776936542719
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.940 Γ— 10⁹⁴(95-digit number)
99409356763442707937…66981543776936542721
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
1.988 Γ— 10⁹⁡(96-digit number)
19881871352688541587…33963087553873085439
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.988 Γ— 10⁹⁡(96-digit number)
19881871352688541587…33963087553873085441
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
3.976 Γ— 10⁹⁡(96-digit number)
39763742705377083174…67926175107746170879
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.976 Γ— 10⁹⁡(96-digit number)
39763742705377083174…67926175107746170881
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:57,848,427 XPMΒ·at block #6,825,540 Β· updates every 60s
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