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Block #1,726,742

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/20/2016, 11:55:32 PM Β· Difficulty 10.7022 Β· 5,076,926 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
969e1b93bdc5ff6f62df4c4f608e357262dc8b95e9f1dc6199167984d6c9339e
View on Chainz β†—

Height

#1,726,742

Difficulty

10.702203

Transactions

1

Size

243 B

Version

2

Bits

0ab3c393

Nonce

1,135,757,872

Timestamp

8/20/2016, 11:55:32 PM

Confirmations

5,076,926

Mined by

⛏️ P2SHAKjaKd2Kxt1buNBYuJDadjFL1cDPsqUE8e

Merkle Root

0072735af3a5c282d52c5b0d448a5fcfb95a8f146f77a9fa0bee1e1d952bd36b
Transactions (1)
Coinbase0072735af3a5c2…ee1e1d952bd36b
1 in β†’ 2 out8.7200 XPM152 B
AKjaKd2K…DPsqUE8eAXbk7f7A…Tx7JECPG
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.

3.233 Γ— 10⁹⁷(98-digit number)
32333112869881370568…84327888095931760639
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
3.233 Γ— 10⁹⁷(98-digit number)
32333112869881370568…84327888095931760639
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.233 Γ— 10⁹⁷(98-digit number)
32333112869881370568…84327888095931760641
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
6.466 Γ— 10⁹⁷(98-digit number)
64666225739762741136…68655776191863521279
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.466 Γ— 10⁹⁷(98-digit number)
64666225739762741136…68655776191863521281
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
1.293 Γ— 10⁹⁸(99-digit number)
12933245147952548227…37311552383727042559
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.293 Γ— 10⁹⁸(99-digit number)
12933245147952548227…37311552383727042561
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
2.586 Γ— 10⁹⁸(99-digit number)
25866490295905096454…74623104767454085119
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.586 Γ— 10⁹⁸(99-digit number)
25866490295905096454…74623104767454085121
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
5.173 Γ— 10⁹⁸(99-digit number)
51732980591810192909…49246209534908170239
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.173 Γ— 10⁹⁸(99-digit number)
51732980591810192909…49246209534908170241
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:57,673,380 XPMΒ·at block #6,803,667 Β· updates every 60s
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