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Block #1,725,777

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/20/2016, 9:14:26 AM Β· Difficulty 10.6972 Β· 5,101,235 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
f58eef9fee431d256c25896bb5b31b77084b4b600d38ca587a43cb634db9fefe
View on Chainz β†—

Height

#1,725,777

Difficulty

10.697202

Transactions

2

Size

689 B

Version

2

Bits

0ab27bdb

Nonce

1,660,750,438

Timestamp

8/20/2016, 9:14:26 AM

Confirmations

5,101,235

Mined by

⛏️ P2SHAbQEZmiBbqvz12JLEmLHvZMkt51wjNafuH

Merkle Root

ebc6b39f1bbc1b0ecbb7abd9294d76c0ae03ca4317c2017e55a270f4ce2f4653
Transactions (2)
Coinbase8a0f7e91bdd2d4…31f6dbfcff1f03
1 in β†’ 1 out8.7400 XPM109 B
AbQEZmiB…1wjNafuH
230ccf87e495a1…3f41e677835c5d
3 in β†’ 1 out6071.9900 XPM490 B
AcDhjHA9…ebukETHz
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.

3.702 Γ— 10⁹⁴(95-digit number)
37028102191191558290…56696314031296846319
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
3.702 Γ— 10⁹⁴(95-digit number)
37028102191191558290…56696314031296846319
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.702 Γ— 10⁹⁴(95-digit number)
37028102191191558290…56696314031296846321
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
7.405 Γ— 10⁹⁴(95-digit number)
74056204382383116580…13392628062593692639
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.405 Γ— 10⁹⁴(95-digit number)
74056204382383116580…13392628062593692641
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
1.481 Γ— 10⁹⁡(96-digit number)
14811240876476623316…26785256125187385279
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.481 Γ— 10⁹⁡(96-digit number)
14811240876476623316…26785256125187385281
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
2.962 Γ— 10⁹⁡(96-digit number)
29622481752953246632…53570512250374770559
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.962 Γ— 10⁹⁡(96-digit number)
29622481752953246632…53570512250374770561
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
5.924 Γ— 10⁹⁡(96-digit number)
59244963505906493264…07141024500749541119
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.924 Γ— 10⁹⁡(96-digit number)
59244963505906493264…07141024500749541121
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:57,860,273 XPMΒ·at block #6,827,011 Β· updates every 60s
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