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Block #190,460

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/2/2013, 12:23:59 PM Β· Difficulty 9.8739 Β· 6,625,785 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
f645faa34eb2b69ab2ba9fb8bef5ee7b0a980b72ff1a77b532d1dbe2a52ec8bf
View on Chainz β†—

Height

#190,460

Difficulty

9.873890

Transactions

2

Size

358 B

Version

2

Bits

09dfb739

Nonce

87,771

Timestamp

10/2/2013, 12:23:59 PM

Confirmations

6,625,785

Mined by

⛏️ P2SHAMjEL5jU5FrR33MFDHGMbVsnwkXWAbZRhp

Merkle Root

e374ad9b62ec55a1f8230fba87076e9247d788d339d1e0227c5ba2f4b7a90c66
Transactions (2)
Coinbasef1a75cf017f5e7…e94ee73fe0dd42
1 in β†’ 1 out10.2500 XPM109 B
AMjEL5jU…XWAbZRhp
e84bc6af113e5b…c11678bb0ebd8a
1 in β†’ 1 out10.2700 XPM159 B
ARA9Q1ay…t4EzMknt
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.

2.955 Γ— 10⁹⁴(95-digit number)
29554985527506270414…56554193368597956959
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
2.955 Γ— 10⁹⁴(95-digit number)
29554985527506270414…56554193368597956959
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.955 Γ— 10⁹⁴(95-digit number)
29554985527506270414…56554193368597956961
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
5.910 Γ— 10⁹⁴(95-digit number)
59109971055012540828…13108386737195913919
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.910 Γ— 10⁹⁴(95-digit number)
59109971055012540828…13108386737195913921
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
1.182 Γ— 10⁹⁡(96-digit number)
11821994211002508165…26216773474391827839
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.182 Γ— 10⁹⁡(96-digit number)
11821994211002508165…26216773474391827841
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
2.364 Γ— 10⁹⁡(96-digit number)
23643988422005016331…52433546948783655679
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.364 Γ— 10⁹⁡(96-digit number)
23643988422005016331…52433546948783655681
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
4.728 Γ— 10⁹⁡(96-digit number)
47287976844010032662…04867093897567311359
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,774,079 XPMΒ·at block #6,816,244 Β· updates every 60s
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