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Block #1,527,202

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/5/2016, 7:26:20 AM Β· Difficulty 10.6071 Β· 5,315,722 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
176596046bc9bf19f1569a70926ea5420201bb25c6eb0fd6a69be99160ab28c7
View on Chainz β†—

Height

#1,527,202

Difficulty

10.607063

Transactions

1

Size

199 B

Version

2

Bits

0a9b6880

Nonce

178,197,133

Timestamp

4/5/2016, 7:26:20 AM

Confirmations

5,315,722

Mined by

⛏️ P2SHAYgRp9JsDP3MiE8miEQuBbxFTwBRM6yrBn

Merkle Root

39deb4caf1f08ebd464adafecdad1c2202752f8f36c1a84ba6400f7c91a21cdf
Transactions (1)
Coinbase39deb4caf1f08e…400f7c91a21cdf
1 in β†’ 1 out8.8700 XPM109 B
AYgRp9Js…BRM6yrBn
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.

8.470 Γ— 10⁹³(94-digit number)
84705538933622927553…00361255066690202769
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
8.470 Γ— 10⁹³(94-digit number)
84705538933622927553…00361255066690202769
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.470 Γ— 10⁹³(94-digit number)
84705538933622927553…00361255066690202771
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
1.694 Γ— 10⁹⁴(95-digit number)
16941107786724585510…00722510133380405539
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.694 Γ— 10⁹⁴(95-digit number)
16941107786724585510…00722510133380405541
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
3.388 Γ— 10⁹⁴(95-digit number)
33882215573449171021…01445020266760811079
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.388 Γ— 10⁹⁴(95-digit number)
33882215573449171021…01445020266760811081
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
6.776 Γ— 10⁹⁴(95-digit number)
67764431146898342042…02890040533521622159
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.776 Γ— 10⁹⁴(95-digit number)
67764431146898342042…02890040533521622161
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
1.355 Γ— 10⁹⁡(96-digit number)
13552886229379668408…05780081067043244319
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.355 Γ— 10⁹⁡(96-digit number)
13552886229379668408…05780081067043244321
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:57,987,740 XPMΒ·at block #6,842,923 Β· updates every 60s
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