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Block #1,534,609

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/10/2016, 8:47:52 AM Β· Difficulty 10.6176 Β· 5,292,465 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
ab7374b36a3d54c1c134cdaa5a27dd47cd70ab9f2c87c4ebe623933d8ed16e18
View on Chainz β†—

Height

#1,534,609

Difficulty

10.617586

Transactions

2

Size

7.62 KB

Version

2

Bits

0a9e1a1e

Nonce

293,372,740

Timestamp

4/10/2016, 8:47:52 AM

Confirmations

5,292,465

Mined by

⛏️ P2SHAPp5crS16aQ15w6mWrRxuzwMKXkzZQ3W2i

Merkle Root

7bbde8a49b07f55237ddd628322768a870633d89df523b5a013a7aac0ed420fb
Transactions (2)
Coinbased30f8a335e5a8a…7ae7b4a31f2e5d
1 in β†’ 1 out8.9400 XPM109 B
APp5crS1…kzZQ3W2i
b7ef230ed579fd…39861c2ef3447f
51 in β†’ 1 out2949.6025 XPM7.42 KB
AXekWzs4…f859ZSYv
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.

6.411 Γ— 10⁹⁢(97-digit number)
64117218458966686229…25032104788838082559
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
6.411 Γ— 10⁹⁢(97-digit number)
64117218458966686229…25032104788838082559
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.411 Γ— 10⁹⁢(97-digit number)
64117218458966686229…25032104788838082561
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
1.282 Γ— 10⁹⁷(98-digit number)
12823443691793337245…50064209577676165119
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.282 Γ— 10⁹⁷(98-digit number)
12823443691793337245…50064209577676165121
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
2.564 Γ— 10⁹⁷(98-digit number)
25646887383586674491…00128419155352330239
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.564 Γ— 10⁹⁷(98-digit number)
25646887383586674491…00128419155352330241
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
5.129 Γ— 10⁹⁷(98-digit number)
51293774767173348983…00256838310704660479
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.129 Γ— 10⁹⁷(98-digit number)
51293774767173348983…00256838310704660481
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
1.025 Γ— 10⁹⁸(99-digit number)
10258754953434669796…00513676621409320959
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.025 Γ— 10⁹⁸(99-digit number)
10258754953434669796…00513676621409320961
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:57,860,775 XPMΒ·at block #6,827,073 Β· updates every 60s
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